Logical Reasoning Ch 4

What is conditional reasoning?

Conditional reasoning is the skill of understanding if/then situations. If one thing happens, then another must happen. The MUST relationship is ironclad; if the sufficient condition occurs, the necessary condition must follow.

Where is conditional reasoning found in Logical Reasoning?

Conditional reasoning is always found in the stimulus, most often in arguments, premise sets, and debates.

What is the sufficient condition in a conditional statement?

The sufficient condition is the “if” part of the conditional. It could occur but doesn’t have to. If present, it activates the conditional statement, and the necessary condition must follow. If absent, the conditional statement is ignored.

What are sufficient indicators?

Sufficient indicators are words like “if” that introduce the sufficient condition. They are all-inclusive, open words. Other indicators exist, and understanding the core if/then relationship is key to avoid confusion from complex language.

What is the main challenge with conditional reasoning?

The challenge is the complex language used to write conditionals, which obscures the basic if/then relationship. Relying only on indicator words can lead to mistakes; understanding the core logic is crucial.

What is the necessary condition in a conditional statement?

The necessary condition is the “then” part of the conditional. It must happen if the sufficient condition occurs, proving the necessary condition when the sufficient condition is present.

What are necessary indicators?

Necessary indicators are words like “then” that introduce the necessary condition. They are ironclad, serious, and restrictive, indicating obligations. “Only if” is a necessary indicator despite containing “if,” where “only” controls the meaning.

What is the contrapositive of a conditional statement?

The contrapositive is: if the necessary condition is absent, the sufficient condition is absent. It’s inherent in the original conditional, requiring no external information, and expresses the same ironclad Must Relationship.

What can you infer from a conditional statement?

You can only infer the original conditional and its contrapositive. The LSAT may trick you into thinking more can be inferred, but only these two are valid. The necessary condition alone doesn’t trigger the conditional.

What happens in different conditional situations?

1. Sufficient condition present: Must have necessary condition.

2. Necessary condition absent: Sufficient condition doesn’t activate.

3. Sufficient condition absent: Nothing happens.

4. Necessary condition present: Nothing happens. Only the first two trigger the conditional.

How do you diagram a conditional relationship?

Use a Must Arrow: Sufficient → Necessary. Steps:

1. Identify a conditional indicator.

2. Draw a Must Arrow.

3. Write the sufficient condition (before the arrow) and necessary condition (after the arrow) using short forms (1–4 letters).

4. Fill in the other side with the remaining statement part.

What is the Must Arrow in conditional diagramming?

The Must Arrow (→) represents the ironclad Must Relationship in conditionals, showing that if the sufficient condition happens, the necessary condition must follow.

How do you diagram the contrapositive of a conditional?

Negate both conditions and switch their places: if the necessary condition is absent (→), the sufficient condition is absent. The slash (/) stays in place, but the conditions swap sides.

When should you diagram the contrapositive?

Diagram the contrapositive when it clarifies the relationship or when chaining multiple conditionals. Otherwise, read the conditional forwards (left to right) or backwards (right to left, negating both sides) mentally.

What are key tips for diagramming conditionals?

Always diagram at first to train your brain. Later, diagram for tricky stimuli or multiple conditionals. Use 1–4 letter abbreviations. Keep a Wrong Answer Journal for incorrect diagrams, noting how language tricked you. Practice builds confidence.

What is The What Test for identifying conditions?

To identify sufficient and necessary conditions in confusing sentences, ask, “What is this sentence trying to promise will happen?” Add “what” to the indicator (e.g., If what?, When what?) to clarify which part is sufficient or necessary.

What are Personalized If/Then statements?

Personalized If/Then statements translate conditionals by putting yourself in the sufficient condition and asking what you know about yourself. If correct, the necessary condition must be true. This clarifies confusing conditionals.

How do you create a Personalized If/Then statement?

1. Understand the sentence’s non-technical meaning.
2. Guess the sufficient condition.
3. Put yourself in the sufficient condition and ask what you know.
4. If the guess is correct, the necessary condition is true; if not, the guess is wrong.

What are conditional chains?

Conditional chains connect multiple conditionals by matching variables, forming a longer sequence (e.g., A → B → C). Chain as you read, combining into one diagram rather than diagramming separately.

How do you diagram conditional chains?

1. Diagram the first conditional (A → B).

2. For the next conditional (B → C), add → C to the end.

3. Result: A → B → C. Read chains straight through (e.g., A → C) or backwards for contrapositive, negating each part.

How many inferences come from a four-part conditional chain?

A four-part chain (e.g., Q → R → S → T) implies 6 inferences (Q → R, Q → S, Q → T, R → S, R → T, S → T) and 6 contrapositives, totaling 12 conditional statements.

What are facilitated chains in conditional reasoning?

Facilitated chains use the contrapositive of one conditional to create a chain when variables don’t match directly. Take the contrapositive of one statement to align variables, then chain (e.g., V → W, X → W becomes V → W → X).

How do you diagram a conditional with AND?

For AND in the sufficient condition (e.g., M and S → E), diagram both conditions with a “+” before the arrow:

M

+ → E.

S

The contrapositive negates and switches to OR:

M

E → or

S

Both sufficient conditions must be present to activate.

How do you diagram a conditional with OR?

For OR in the necessary condition (e.g., F → C or IF), diagram with “or” after the arrow:

C

F → or

IF

The contrapositive negates and switches to AND:

C

+ → F.

IF

Both necessary conditions must be absent to block the sufficient condition.

How do you diagram Neither/Nor in conditionals?

Neither/Nor means “not this and not that.” Diagram as

X

+

Y

representing both conditions negated together, not as OR.

What does “If and Only If” mean, and how is it diagrammed?

“If and Only If” means both sides are sufficient and necessary for each other. Diagram with a double arrow (A ↔ B). Each term can be on either side, and both are always together. Contrapositive negates both: A + B.

What does Either/Or mean on the LSAT?

Either/Or is an inclusion rule meaning at least one of two things must happen, not neither. It allows both or one but not zero. Diagram as a conditional: negate one part for the sufficient condition, other part for the necessary (e.g., cake → ice cream).

How can you make Either/Or easier?

When you see EITHER/OR, you should make it into a conditional like this so that it clearly shows that If one thing is missing, then the other one has to happen.

The LSAT doesn’t always write this as an “if/then” rule. But to make it easier to understand and figure out what must happen, turn it into a conditional (an if/then sentence) that forces inclusion.

How do you diagram an Either/Or statement?

1. Negate one half of the statement and place it in the sufficient condition.

2. Place the other half in the necessary condition. Either direction works, as they are contrapositives of each other.

What are exclusion indicators in conditionals?

Exclusion indicators (e.g., no, none, nobody, never) show two things cannot both be true. Diagram as a conditional: one side in the sufficient condition, negate the other for the necessary condition (e.g., pocket square → surrender).

How do you diagram an exclusion statement?

1. Choose one side of the statement for the sufficient condition.

2. Negate the other side and place it in the necessary condition. Either direction works, as they are equivalent.

How do inclusion and exclusion statements differ?

Inclusion (e.g., Either/Or) means at least one thing must happen, allowing both or one but not zero. Exclusion (e.g., none, never) means two things cannot both happen; if one is true, the other cannot be.

How do you clarify inclusion and exclusion statements?

Translate into a personalized if/then statement. Understand the sentence in plain terms, then ask if it requires at least one thing (inclusion: negate one for sufficient, other for necessary) or prohibits both (exclusion: one for sufficient, negate other for necessary).

What does Unless mean in conditionals?

Unless is a conditional exception indicator, showing the only way to escape the normal rule. The exception is the necessary condition, and the negated normal rule is the sufficient condition.

How do you diagram an Unless statement?

1. Place the exception (after Unless) in the necessary condition.

2. Negate the normal rule and place it in the sufficient condition. Diagram as: Negated normal → Exception.

What does Some mean in conditional reasoning?

Some means a quantity of one or more (1% to 100%). For example, some cookies being salted shortbread could mean 1 to all cookies.

What does Most mean in conditional reasoning?

Most means any quantity in the majority (51% to 100%). For example, most cookies containing dark chocolate could mean 3, 4, or all 5 in a group of 5.

Since Some and Most refer to quantity, How can you diagram them?

Even though Some and Most refer to quantity, you can still diagram them like you do with regular conditionals.

How do you diagram Some and Most statements?

Place the target (after Some/Most) in the sufficient condition. Use a Some Arrow (←s→) for Some and a Most Arrow (m→) for Most. Place the trait in the necessary condition. These arrows indicate possibility, not certainty.

What is the Some Arrow, and why is it used?

The Some Arrow (←s→) is used for Some statements because Some allows less than 100%, showing a possible but not guaranteed relationship between the sufficient and necessary conditions.

What is the Most Arrow, and how is it read?

The Most Arrow (m→) is used for Most statements, indicating a majority relationship. Read as an if/then statement: “If I’m in the sufficient group, most of me have the necessary trait.”

Can you take the contrapositive of a Some statement?

No, you cannot take the contrapositive of a Some statement because Some doesn’t guarantee a necessary condition, so negating it doesn’t lead to a valid inference.

What does Not All mean in conditional reasoning?

Not All is a Some indicator meaning some of the target don’t have the described quality. Diagram as: Target ←s→ Not Quality, indicating at least one lacks the trait.

What is the implication of a Most statement?

A Most statement (e.g., Most A are B) implies Some B are A, but not Most B are A. It describes the sufficient group (A), not the necessary group (B), so only a Some relationship can be inferred for B.

What are the three valid Some/Most inferences?

1. A ←s→ B → C infers A ←s→ C (extend Some Arrow).
2. A m→ B → C infers A m→ C (extend Most Arrow).
3. A m→ B, A m→ C infers B ←s→ C (Some overlap between necessary groups).

What are the limits of Some/Most inferences?

Only the three specified Some/Most chains lead to valid inferences. Any other combination is invalid, so don’t infer beyond these patterns.