LSAT - Formal Logic - Conditional Statements

Two Most Common Translations

- Not X unless Y = X only if Y

- If X then Y = X → Y

Unless (until, without) Rules

/the way things always are → exception (the target of unless)

If, But Only If (all and only, but not otherwise, when and only when) Definition

Indicate a bi-conditional (<—>) relationship.

If, But Only If Format

"X if, but only if Y" can be written:

a. If X → Y

b. If Y → X

c. Or alternatively X ⟷ Y

No (none, never, not, nobody) Rules:

Choose one variable, negate it, and put it in the necessary condition. The remaining variable goes in the sufficient

Either/Or Rules:

Choose one variable, negate it and put it in the sufficient condition. Put the other half in the necessary.

Some Inference Format

A ←s→ B → C = A ←s→ C

Some Inference Formal Logic

If I'm A, then some of me is B; if I'm B, then I must lead to C. So some of A is C

Most Inference Format

1. A —m→ B → = A —m→ C

2. A—m→ B

A —m→ C = B ←s→ C

Most Inference Formal Logic

1. If I'm A, then most of me is B. If I'm B, then I must lead to C. So, most of A is C

2. If I'm A, then most of me is B and C. So, if I'm B, then some of me is C

And Rules:

both terms are needed for a sufficient condition to trigger/for a necessary condition to be fulfilled. Use a + between the two variables to represent

Or Rules:

At least one of the terms (or sometimes both for necessary) is needed for a sufficient condition to trigger a result or for a necessary condition to be fulfilled. Use an Or between the two variables

And/Or Contrapositive:

They are the contrapositives of each other. Negate and flip the variables, and change it to “And” (if starting with Or")/”Or” (if starting with And”)

"But" Functions as...

"and" in Formal Logic

"But Not Both" Or Statements

- Means the "or" is mutually exclusive and only one term can be the outcome.

- List as two separate shorthand statements.

"But Not Both" Example

- If A then B or C, but not both.

- If A then B or C.

- If A then not B and C.

Negated And/Or - Neither/Nor

Neither X nor Y means “Not X and Not Y.”

Making Valid Deductions from Conditional Statements - Same Sufficient Term

a. If A, then B.

b. If A, then C.

c. Deduction: If A, then both B and C.

Making Valid Deductions from Conditional Statements - Same Necessary Term

a. If T, then V.

b. If W, then V

c. Deduction: If either T or W (or both), then V

Making Valid Deductions from Conditional Statements - Same Term in both the Sufficient & Necessary

a. If X, then Y

b. If Y, then Z

c. Deduction: If X, then Z.

Making Valid Deductions from Conditional Statements Containing an "Exclusive Or" Provision. - Format

1. Shorthand: If A then B or C

2. Contrapositive Shorthand: If not B & Not C then Not A

3. Shorthand Exclusive: If A then NOT [B and C]

4. Contrapositive Exclusive: IF [B and C] then NOT A

Determining the Valid Deduction from a Conditional Statement with the "If X then /Y" Structure. - Format

1. If C then /D

2. If D then /C

3. Both C and D Out.

Determining the Valid Deduction from a Conditional Statement with the "If /X then Y" Structure. - Format

1. If /E then F

2. If /F then E

3. Both E and F In.