Conditional Reasoning (Loopholes)

Conditional Statement

An "If/then" statement, made up of a sufficient condition and a necessary condition. If the sufficient condition happens, the necessary condition MUST also occur.

Sufficient Condition Indicator Attributes

Words like If, When(ever), Any(time), All, Every(time), in order to, people who, each

They are all open, inviting words.

Necessary Condition Indicator Attributes

The necessary condition is literally necessary.

Words like then, must, necessary, required, only (if), depends, need (to), have to, essential, precondition

Notice how all the indicators are ironclad. They are serious, restrictive, and obligatory

Contrapositive

If the necessary condition is absent, then the sufficient condition MUST be absent.

The original statement and it's contrapositive are all you know from your conditional relationship. That's all.

Remember: The presence of a necessary condition doesn't make anything happen.

Example: C -> D. Contrapositive = ~D -> ~C

Situation: The sufficient condition is present. What has to happen?

The necessary condition MUST be present.

EX: I'm breathing so there must be air.

Situation: The necessary condition is absent. What has to happen?

The sufficient condition MUST be missing.

EX: There's no air, so I can't breathe.

Situation: The necessary condition is present. What has to happen?

Nothing!

There's air around, but I don't have to be breathing (could be holding breath)

Situation: The sufficient condition is missing. What has to happen?

Nothing!

Ex: I'm not breathing, but we don't know if there's air around. (Could be underwater or in space).

What does this diagram mean? X -> Y

X is the sufficient condition, Y is the necessary condition. If X is present, then Y must be also. It is a "must" relationship.

We also know that if Y is not present, then X cannot be present.

Explain the "What" test

"What" is the indicator referring to? Used when you don't know which is the sufficient or necessary condition. You see an indicator, ask yourself "what" the indicator is referring to.

Ex: "Air is REQUIRED for breathing." REQUIRED is a necessary condition indicator. So you ask yourself "What is required?" Air is required. So -> A. Then you know B -> A.

The Personalized If/Then

Make a habit of translating conditionals into personalized if/then statements.

1. Try to understand the casual, non-conditional meaning of the sentence.

2. Take a guess at which half of the statement is the sufficient condition.

3. Put yourself in your guess' situation and ask what you know about yourself.

4. If your guess is right, you will know that the necessary condition has to pertain.

And/Or

Ex: "If we eat pie AND take a bath, we will be happy."

P

+ -> H

B

Contrapositive:

~P

~H -> or

~B

Ex: "If you are a Communist, you are stupid or ugly"

S

D -> or

U

Contrapositive:

~S

+ -> ~D

~U

REMEMBER: When looking at the contrapositive, always flip "Or" and "and."

"If and only if"

A marriage between sufficient and necessary conditions.

It means the two variables (conditions) go hand in hand. If one of them happens, the other must happen too.

EX: We will compromise if and only if I get everything I want.

Part 1: We will compromise if I get everything I want. IF is a sufficient indicator, SO:

I get everything I want -> Compromise

Part 2: We will compromise only if I get everything I want. ONLY IF is a necessary indicator, SO:

Compromise -> I get everything I want.

Both conditions serve as a necessary and sufficient condition.

It is diagrammed as: C <--> GEIW

Other synonyms to "if and only if:"

if but only if, all and only, but not otherwise, when and only when

Either/Or

Implies that you must have at least one or the other, possibly both.

To Diagram:

1. Take one half of the statement and negate it. It becomes your sufficient condition.

2. Place the other half as your necessary condition.

Exclusion Indicators

If you have an exclusion indicator, you have to choose between the two variables. If you have one, you can't have the other.

Rephrasing as an If/Then is crucial.

To Diagram:

1. Choose a side of the statement, put it as your sufficient condition.

2. Negate the other side and put it as your necessary condition.

Unless

"This is the way it is, UNLESS this ONE thing happens."

Rule: ~[the way things are] -> exception

To Diagram:

1. The target of "unless" is the exception. Use as necessary condition.

2. The other half of the statement is the way things are. Negate the way things are and put that as your sufficient indicator.

Some/Most

Some/Most are some of the hardest LSAT questions.

Some = between 1% and 100%

Most = between 51% and 100% (majority)

To Diagram:

1. Some/Most always goes before their target and their target goes straight in the sufficient condition.

Some Arrow <-S->

Must Arrow -M->

Some/Most Inferences

A <-S-> B -> C Inference: A <-S-> C

A -M-> B -> C Inference: A -M-> C

A -M-> B Inference: B <-S-> C

A -M-> C