Translating If-Then Statements (Beginner)

To maintain military deterrence, a nation would have to be believed to have retaliatory power so great that a potential aggressor nation would have reason to think that it could not defend itself against such retaliation.

MD → GRP / not GRP → not MD

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement, we can find a "requirement." A nation "would have to" believe it has "retaliatory power so great" that aggressors would fear they couldn't defend themselves. That's a requirement for maintaining military deterrence. So, that requirement must go on the "then" side. We can shorten that requirement to "GRP" for "great retaliatory power." We shortened the other part to "MD" for "maintain deterrence." (PT1, Sec. 3, Q4)

A would-be aggressor nation can be deterred from attacking only if it has certain knowledge that it would be destroyed in retaliation by the country it attacks.

AD → KD / not KD → not AD

Explanation: This statement features the keyword "only," one of the "then" keywords. "Only" refers to having "certain knowledge that it would be destroyed in retaliation by the country it attacks." That condition should go on the "then" side. We abbreviated that condition to "KD" for "know destroyed." We shortened the other part to "AD" for "aggressor deterred."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." A nation must have "certain knowledge that it would be destroyed in retaliation by the country it attacks" to be deterred. That's a requirement for being deterred. That requirement would go on the "then" side, and the other part would go on the "if" side. (PT1, Sec. 3, Q4)

One nation's failing to attack another establishes that the nation that fails to attack believes that it could not withstand a retaliatory attack from the other nation.

not A → not BWR / BWR → A

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement we can find a "trigger" and an "outcome." The trigger is "one nation failing to attack another." We could put an "if" in front of that claim without changing the statement's meaning: "If one nation fails to attack another, then the nation that fails to attack believes it could not withstand a retaliatory attack from another nation." That trigger should go on the "if" side. We abbreviated that to "not A" for "not attack." The "outcome" is establishing the nation's belief "that it could not withstand a retaliatory attack." (You could also think of this as a requirement.) We abbreviated that to "not BWR" for "not believe (it would) withstand retaliation." That should go on the "then" side. (PT1, Sec. 3, Q4)

Maintaining maximum deterrence from aggression by other nations requires that a nation maintain a retaliatory force greater than that of any other nation.

MMD → MGR / not MGR → not MMD

Explanation: This statement features the keyword "requires," one of the "then" keywords. "Requires" refers to a nation maintaining "a retaliatory force greater than that of any other nation." That condition should go on the "then" side. We abbreviated that condition to "MGR" for "maintain (the) greatest retaliation." We shortened the other part to "MMD" for "maintain maximum deterrence." (PT1, Sec. 3, Q4)

In each field of science, it is possible to distinguish scientific information from advanced technological knowledge that is of commercial or national-security value.

Explanation: This statement features the keyword "each," one of the "if" keywords. "Each" refers to "field of science." That condition should go on the "if" side. We abbreviated that condition to "FS" for "field (of) science." We shortened the other part to "DST" for "distinguish science (from) technology."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal." We can add an "all" in front of "field of science" without changing the meaning of the statement: "In all fields of science, it is possible to distinguish scientific information from advanced technological knowledge that is of commercial or national-security value." The universal would go on the "if" side, and the other part would go on the "then" side. (PT1, Sec. 3, Q10)

When a large business with multiple, linked computer systems uses identical operating system software on all of its computers, a computer vandal who gains access to one computer automatically has access to the data on all the computers.

LIC → VAD / not VAD → not LIC

Explanation: This statement features the keyword "when," one of the "if" keywords. "When" refers to having "a large business with multiple, linked computer systems [that] uses identical operating system software on all of its computers." That condition should go on the "if" side. We abbreviated that condition to "LIC" for "linked, identical computers." We shortened the other part to "VAD" for "vandals access data."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "trigger" and an "outcome." The trigger is "when a large business with multiple, linked computer systems uses identical operating system software on all of its computers." We could put an "if" in front of that claim without changing the statement's meaning: "If a large business with multiple, linked computer systems uses identical operating system software on all of its computers ..." That trigger should go on the "if" side. The outcome is "a computer vandal who gains access to one computer automatically has access to the data on all the computers." That goes on the "then" side. (PT1, Sec. 3, Q15)

Unless a railroad serves its customers well, it will not be a successful business.

not SCW → not S / S → SCW

Explanation: This statement features the keyword "unless," one of the "if not" keywords. So, we should put a "not" on the "if" side. Then, we can slot the conditions ("SCW" for "serve customers well" and "not S" for "not successful") on either side of the arrow. That would give us "not SCW → not S" or "S → SCW" (since the two "nots" cancel each other out on the "if" side). These are flipsides of each other, and both are valid ways to diagram the claim.

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." The requirement is "serving its customers well." The requirement would go on the "then" side. However, you may have initially written, "not S → SCW" ("if it's not successful, then it must serve its customers well"), which doesn't make much sense. If you take the "not" away on the "if" side, you'll have an accurate diagram: "S → SCW" ("if it is successful, then it must serve its customers well"). (PT1, Sec. 1, Q19)

Picture-winged drosophilids are found only in the Hawaiian islands.

PWD → H / not H → not PWD

Explanation: This statement features the keyword "only," one of the "then" keywords. "Only" refers to "Hawaiian islands." That condition should go on the "then" side. We abbreviated that to "H" for "Hawaii." We shortened the other part to "PWD" for "picture-winged drosophilids."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." A picture-winged drosophilid must be in "the Hawaiian islands." That requirement would go on the "then" side, and the other part would go on the "if" side. (PT1, Sec. 4, Q2)

A society that has no laws has no crimes.

not SL → not C / C → SL

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement, we could find a "universal." We can add an "all" in front of "society" without changing the statement's meaning: "All societies that have no laws have no crimes." The universal would go on the "if" side. The other part would go on the "then" side. We shortened the universal to "not L" for "not society (with) laws." We shortened the other part to "not C" for "not crimes." (PT1, Sec. 4, Q6)

Every member of the police force is qualified to work on combating the city's drug problem.

P → QDP / not QDP → not P

Explanation: This statement features the keyword "every," one of the "if" keywords. "Every"

refers to "member[s] of the police force." That condition should go on the "if" side. We abbreviated that condition to "P" for "police." We shortened the other part to "QDP" for "qualified (for) drug problem."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal." We can add an "all" in front of "member of the police force" without changing the statement's meaning: "All members of the police force are qualified to work on combating the city's drug problem." The universal would go on the "if" side. The other part would go on the "then" side. (PT2, Sec. 2, Q3)

The police cannot continue writing as many speeding tickets as ever while diverting resources to combating drug-related crime.

WST→ not DRD / DRD → not WST

Explanation: This statement features the keyword "cannot," one of the "then not" keywords. So, we should put a "not" on the "then" side. Then, we can slot the conditions ("WST" for "write speeding tickets" and "DRD" for "diverting resources (to) drugs") on either side of the arrow. That would give us, "WST→ not DRD," or, "DRD → not WST." These are flipsides of each other, and both are valid ways to diagram the claim.

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "trigger" and "outcome." The "trigger" is "diverting resources to combating drug-related crime." We could put an "if" in front of that claim without changing the statement's meaning: "The police cannot continue writing as many speeding tickets as ever if they divert resources to combating drug-related crime." The outcome is "cannot continue writing as many speeding tickets as ever." The trigger goes on the "if" side, and the outcome would go on the "then" side. (PT2, Sec. 2, Q3)

Any art theft committed at the direction of a single individual results in a pattern that defies rational analysis.

ATI → DRA / not DRA → not ATI

Explanation: This statement features the keyword "any," one of the "if" keywords. "Any" refers to "art theft[s] committed at the direction of a single individual." That condition should go on the "if" side. We abbreviated that condition to "ATI" for "art theft (by) individual." We shortened the other part to "DRA" for "defies rational analysis."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal." We can change "any" to "all" without changing the statement's meaning: "All art thefts committed at the direction of a single individual result in patterns that defy rational analysis." The universal would go on the "if" side. The other part would go on the "then" side. (PT2, Sec. 4, Q1)

Superior physical fitness produces superior health.

SF → SH / not SH → not SF

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement we can find a "trigger" and an "outcome." The trigger is attaining "superior fitness." We could put an "if" in front of that claim without changing the statement's meaning: "If one attains superior fitness, then one attains superior health." That trigger should go on the "if" side. We abbreviated it to "SF" for "superior fitness." The "outcome" is attaining that "superior health." We abbreviated that to "SH." That should go on the "then" side. (PT3, Sec. 2, Q3)

The number of white blood cells will increase radically if behavior is consistently magnanimous.

CM → WBC↑ / not WBC↑ → not CM

Explanation: This statement features an "if." "If" refers to "behavior [that] is consistently magnanimous." That should go on the "if" side. We shortened that to "CM" for "consistently magnanimous." The other part is "number of white blood cells will increase radically." We shortened that to "WBC↑" for "white blood cells increase" and put that on the "then" side. (PT3, Sec. 4, Q4)

The high costs of opera production necessitate reliance on large corporate sponsors.

OP → LCS / not LCS → not OP

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement, we can find a "requirement." One must rely "on large corporate sponsors" to produce an opera. Large corporate sponsors are a requirement for an opera production. So, that requirement must go on the "then" side. We can shorten that requirement to "LCS." We shortened the other part to "OP" for "opera production." (PT3, Sec. 4, Q5)

Without the support of large corporate sponsors, opera companies could not afford to produce any but the most famous of operas.

not LCS → OFO / not OFO → LCS

Explanation: This statement features the keyword "without," one of the "if not" keywords. So, we should put a "not" on the "if" side. The fist condition can be shortened to "LCS" for "large corporate sponsors." We used a positive mindset to translate the second condition, "could not afford to produce any but the most famous of operas," to "only famous operas" or "OFO." We could slot these conditions on either side of the arrow. That would give us "not LCS → OFO" or "not OFO → LCS." These are flipsides of each other, and both are valid ways to diagram the claim.

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." The requirement is "large corporate sponsors." The requirement would go on the "then" side. However, you may have initially written, "OFO → LCS" ("if you can only afford famous operas, then you must have large corporate sponsors"), which doesn't make much sense. If you add a "not" on the "if" side, you'll have an accurate diagram: "not OFO → LCS" ("if you can afford to not only perform famous operas, then you must have large corporate sponsors"). (PT3, Sec. 4, Q5)

The government will be able to recapture capable administrators by raising salaries to a level comparable to those of the private sector.

RS → RCA / not RCA → not RS

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement, we can find a "trigger" and an "outcome." The trigger is "raising salaries to a level comparable to those of the private sector." We could put an "if" in front of that claim without changing the statement's meaning: "The government will be able to recapture capable administrators if it raises salaries to a level comparable to those of the private sector." That trigger should go on the "if" side. We abbreviated it to "RS" for "raises salaries." The "outcome" is that "the government will be able to recapture capable administrators." We abbreviated that to "RCA" for "recapture capable administrators." That should go on the "then" side. (PT3, Sec. 4, Q19)

People who moved from jobs in government administration to private-sector management would choose to change careers again.

MPS → CCA / not CCA → not MPS

Explanation: This statement features the keyword "people who," one of the "if" keywords. "People who" refers to those who move "from jobs in government administration to private-sector management." That condition should go on the "if" side. We abbreviated that condition to "MPS" for "move (to) private sector." We shortened the other part to "CCA" for "change careers again."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal." We can add an "all" in front of "people who moved from jobs in government administration to private-sector management" without changing the statement's meaning: "All people who moved from jobs in government administration to private-sector management would choose to change careers again." The universal would go on the "if" side, and the other part would go on the "then" side. (PT3, Sec. 4, Q19)

A nation that owes money to another nation cannot be a world leader.

OM → not WL / WL → not OM

Explanation: This statement features the keyword "cannot," one of the "then not" keywords. So, we should put a "not" on the "then" side. Then, we can slot the conditions ("OM" for "owes money" and "WL" for "world leader") on either side of the arrow. That would give us "OM → not WL" or "WL → not OM." These are flipsides of each other, and both are valid ways to diagram the claim.

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal." We can add an "all" in front of "nation that owes money to another nation" without changing the statement's meaning: "All nations that owe money to another nation cannot be world leaders." The universal would go on the "if" side, and the other part would go on the "then" side. (PT4, Sec. 1, Q5)

A nation that is a world leader can borrow from another nation as long as that other nation does not set the terms of the dealings between the two nations.

not LST → WLB / not WLB → LST

Explanation: This statement does not feature any of the 20 most common keywords. It's also difficult to T.O.U.R. this statement. Is the universal "all" nations that are world leaders? Or does "as long as the other nation does not set the terms of the dealings between the two nations" trigger an outcome?

When a statement features this much ambiguity, it can help translate it both ways and determine which is more consistent with the original claim. "If a world leader borrows money from another nation, then the other nation does not set the terms of dealings between the two." Does that seem consistent with the original claim? What about the other way? "If the other nation does not set the terms of dealings between the two, then a world leader can borrow money from another nation."

We'd argue that the second is more consistent with the original claim. The original claim makes the other nation not setting the terms of the dealings seem like a condition that enables the world leader to borrow money. In other words, this condition is the trigger that allows the world leader to borrow. Therefore, not setting the terms of the dealings should go on the "if" side. We shortened that to "not LST" for "lender (does) not set terms." We shortened the "then" part to "WLB" for "world leader borrow."

If you had trouble assessing this statement and think you can memorize one more keyword, you can add "as long as" to your list of "if" keywords. (PT4, Sec. 1, Q5)

Legumes are currently the only crops that produce their own supply of fixed nitrogen.

PNS → L / not L → not PNS

Explanation: This statement features the keyword "the only." Technically, "the only" refers to "then" conditions. In this case, "legumes" are "the only" crop that can produce their own supply of fixed nitrogen, so "L" should go on the "then" side. However, most people find it easier to remember that "the only" comes before "if" conditions in a sentence. Therefore, "crops that produce their own supply of fixed nitrogen" — or "PNS" for "produce nitrogen supply" — should go on the "if" side.

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." For a crop to "produce their own supply of fixed nitrogen," it must be a legume. In other words, being a legume is a requirement for producing a fixed nitrogen supply. That requirement would go on the "then" side, and the other part would go on the "if" side. (PT4, Sec. 1, Q10)

Government intrusion into private businesses is justified only when individuals might be harmed.

GIJ → IMH / not IMH → not GIJ

Explanation: This statement features the keyword "only," one of the "then" keywords. "Only" refers to instances "when individuals might be harmed." That condition should go on the "then" side. We abbreviated that condition to "IMH" for "individuals might (be) harmed." We shortened the other part to "GIJ" for "government intrusion justified."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." For a government's intrusion into private businesses to be justified, there must be a chance that individuals could be harmed. In other words, the chance that individuals could be harmed is a requirement for government intrusion. That requirement would go on the "then" side, and the other part would go on the "if" side. (PT4, Sec. 1, Q11)

A scientific model that contains many elements is not a good theory.

MME → not GT / GT → not MME

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement, we could find a "universal." We can add an "all" in front of "scientific model" without changing the statement's meaning: "All scientific models that contain many elements are not good theories." The universal would go on the "if" side. The other part would go on the "then" side. We shortened the universal to "MME" for "model (with) many elements." We shortened the other part to "not GT" for "not good theory." (PT4, Sec. 4, Q9)

The new highway would have no benefits for Plainsville other than attracting new business.

NHB → ANB / not ANB → not NHB

Explanation: This statement does not feature any of the 20 most common keywords. It's also difficult to T.O.U.R. this statement. Is the universal "all" new highways? Is "attracting new business" a trigger or a requirement?

When a statement features this much ambiguity, it can help translate it both ways and determine which is more consistent with the original claim. "If a new highway has no benefits, then it is attracting new business." Does that seem consistent with the original claim? What about the other way? "If a new highway is attracting new business, then it has no benefits."

We'd argue that neither formation is consistent with the original. When that happens, try adding a "not" or taking one away. There's a "no" before benefits, so let's try taking that away. "If a new highway has any benefits, then it is attracting new business." That seems consistent with the original claim, which makes it sound like attracting new business is the only benefit the highway could have. So, we shortened "a new highway has benefits" to "NHB" for "new highway (has) benefits." We slotted that into the "if" side. We also shortened "attracting new business" to "ANB" and slotted that on the "then" side.

If you had trouble assessing this statement and think you can memorize one more keyword, you can add "other than" to your list of "if not" keywords. (PT5, Sec. 1, Q3)

Anyone planning to use resources collected from a group must consult the members of the group before using the resources.

UGR → CGM / not CGM → not UGR

Explanation: This statement features "anyone," which is a variation of the keyword "any," one of the "if" keywords. "Anyone" refers to those who are "planning to use resources collected from a group." That condition should go on the "if" side. We abbreviated that condition to "UGR" for "use group resources." This statement also features "must," one of the "then" keywords. "Must" refers to needing to "consult the members of the group before using the resources." That condition should go on the "then" side. We abbreviated that condition to "CGM" for "consult group members."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal" and a "requirement." The universal refers to "all" people who are "planning to use resources collected from a group." The universal would go on the "if" side. Additionally, "consult the members of the group before using the resources" is a requirement for using group resources. That requirement should go on the "then" side. (PT5, Sec. 1, Q4)

Only politicians who rely on their offices for income tend to support policies that advance their own selfish interests.

SSP → ROI / not ROI → not SSP

Explanation: This statement features the keyword "only," one of the "then" keywords. "Only" refers to having "politicians who rely on their offices for income." That condition should go on the "then" side. We abbreviated that condition to "ROI" for "rely (on) office's income." We shortened the other part to "SSP" for "support selfish policies."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." A politician must "rely on their offices for income" to support a policy that advances their own selfish interest. That's a requirement for supporting such a policy. That requirement would go on the "then" side, and the other part would go on the "if" side. (PT6, Sec. 1, Q19)

No worker's full potential will ever be realized.

W → not FPR / FPR → not W

Explanation: This statement features the keyword "no" at the beginning of the statement, which means the "no" functions like one of the "then not" keywords. So, we should put a "not" on the "then" side. Then, we can slot the conditions ("W" for "worker" and "FPR" for "full potential realized") on either side of the arrow. That would give us "W → not FPR" or "FPR → not W." These are flipsides of each other, and both are valid ways to diagram the claim.

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "universal." This claim applies to "all" workers. However, we must infer that all works will not realize their full potential. This universal goes on the "if" side, and "not realizing their full potential" goes on the "then" side. (PT7, Sec. 4, Q3)

The consistency of ice cream is adversely affected by even slight temperature changes in the freezer.

TC → CAA / not CAA → not TC

Explanation: This statement does not feature any of the 20 most common keywords. If we take a T.O.U.R. through the statement we can find a "trigger" and an "outcome." The trigger is a "slight temperature changes in the freezer." We could put an "if" in front of that claim without changing the statement's meaning: "The consistency of ice cream is adversely affected if there are even slight temperature changes in the freezer." That trigger should go on the "if" side. We abbreviated it to "TC" for "temperature changes." The "outcome" is that the "consistency of ice cream is adversely affected." We abbreviated that to "CAA" for "consistency adversely affected." That should go on the "then" side. (PT7, Sec. 4, Q15)

The poetry editor cannot recognize the poems submitted by Harry Trevalga as his unless Trevalga's name is attached to them.

not TNA → not RTP / RTP → TNA

Explanation: This statement features the keyword "unless," one of the "if not" keywords. This statement also features the keyword "cannot," one of the "then not" keywords. When we have an "if not" keyword and another keyword, it's easier to replace the "if not" keyword with "if not." So, we can translate this claim to: "The poetry editor cannot recognize the poems submitted by Harry Trevalga as his if Trevalga's name is not attached to them." We can shorten the "if' part to "not TNA" for "Trevalga's name (is) not attached." We can shorten the other part to "not RTP" for "not recognize Trevalga's poems."

If we didn't use the keywords to diagram this, we could instead take a T.O.U.R. through the statement and find a "requirement." The requirement is Trevalga's name being attached to Trevalga's poems. The requirement would go on the "then" side. However, you may have initially written, "not RTP → TNA" ("if the editor does not recognize Trevalga's poems, then Trevalga's name was attached"). That doesn't make much sense. If you take the "not" away on the "if" side, you'll have an accurate diagram: "RTP → TNA" ("if the editor recognizes Trevalga's poems, then Trevalga's name was attached"). (PT8, Sec. 1, Q6)

A contract, whether expressed or unexpressed, exists when two parties engage with each other for the reciprocal transfer of benefits.

ATB → CE / not CE → not ATB

Explanation: This statement features the keyword "when," one of the "if" keywords. "When" refers to having "two parties engaging with each other for the reciprocal transfer of benefits." That condition should go on the "if" side. We abbreviated that condition to "ATB" for "agree (to) transfer benefits." We shortened the other part to "CE" for "contract exists."

If we didn't use the keyword to diagram this, we could instead take a T.O.U.R. through the statement and find a "trigger" and an "outcome." The trigger is "when two parties engage with each other for the reciprocal transfer of benefits." We could replace "when" with "if" without changing the statement's meaning: "A contract, whether expressed or unexpressed, exists if two parties engage with each other for the reciprocal transfer of benefits." That trigger should go on the "if" side." The outcome is "a contract, whether expressed or unexpressed, exists." That goes on the "then" side. (PT10, Sec. 1, Q17)