LSAT Analytical Reasoning Conditional Logic Rules Quiz

1. If P then Q. If Q then R. What can you conclude if P is true?

R must be true

R might be true

R must be false

No conclusion about R

By chaining: P → Q → R. If P is true, Q is true; if Q is true, R is true.

Explanation

By chaining: P → Q → R. If P is true, Q is true; if Q is true, R is true.

2. The contrapositive of 'If not A then B' is:

If not B then A

If B then not A

If A then not B

If not B then not A

Contrapositive of (¬A → B) is (¬B → A). A conditional and its contrapositive are logically equivalent.

Explanation

Contrapositive of (¬A → B) is (¬B → A). A conditional and its contrapositive are logically equivalent.

3. If X or Y must be true, and X is false, what follows?

Y must be true

Y must be false

Y might be true or false

X must be true

In a disjunction (X or Y), if one disjunct is false, the other must be true for the statement to hold.

Explanation

In a disjunction (X or Y), if one disjunct is false, the other must be true for the statement to hold.

4. If not S is sufficient for T, which statement is equivalent?

If T then not S

If not T then S

If S then not T

If T then S

Not S sufficient for T means (¬S → T). The contrapositive is (¬T → S).

Explanation

Not S sufficient for T means (¬S → T). The contrapositive is (¬T → S).

5. When is 'If A then B' false?

When A is true and B is false

When A is false and B is true

When both A and B are false

When A is true and B is true

A conditional is false only when the antecedent (A) is true and the consequent (B) is false.

Explanation

A conditional is false only when the antecedent (A) is true and the consequent (B) is false.

6. If all M are N, and all N are O, what can you conclude?

All M are O

All O are M

Some M are O

No M are O

Transitive property: M ⊆ N and N ⊆ O imply M ⊆ O.

Explanation

Transitive property: M ⊆ N and N ⊆ O imply M ⊆ O.

7. If P is necessary for Q, which statement is true?

If Q then P

If P then Q

If not P then not Q

Both (a) and (c)

P necessary for Q means Q → P. The contrapositive ¬P → ¬Q is also true.

Explanation

P necessary for Q means Q → P. The contrapositive ¬P → ¬Q is also true.

8. If either C or D is selected, but not both, which scenario violates this rule?

C selected, D not selected

C not selected, D selected

Both C and D selected

Neither C nor D selected

Exclusive or (C XOR D) is false when both are true. Scenarios (a) and (b) satisfy it; (c) and (d) violate it.

Explanation

Exclusive or (C XOR D) is false when both are true. Scenarios (a) and (b) satisfy it; (c) and (d) violate it.

9. If G is sufficient for H, and H is sufficient for I, what must be true?

G is sufficient for I

I is sufficient for G

G and I are equivalent

H is necessary for both G and I

G sufficient for H (G → H) and H sufficient for I (H → I) chain to G → I.

Explanation

G sufficient for H (G → H) and H sufficient for I (H → I) chain to G → I.

10. The statement 'Not all R are S' is equivalent to:

All R are not S

Some R are not S

No R are S

Some R are S

Not all R are S means at least one R is not S, which is 'Some R are not S.'

Explanation

Not all R are S means at least one R is not S, which is 'Some R are not S.'

11. If exactly one of K or L must be true, and K is true, what follows?

L must be true

L must be false

L can be either true or false

K must be false

Exactly one constraint means K and L have opposite truth values. If K is true, L must be false.

Explanation

Exactly one constraint means K and L have opposite truth values. If K is true, L must be false.

12. If no U are V, what is the contrapositive?

No V are U

All U are not V

All V are not U

Some U are V

No U are V means U and V are mutually exclusive. The statement is symmetric: if no U are V, then no V are U.

Explanation

No U are V means U and V are mutually exclusive. The statement is symmetric: if no U are V, then no V are U.

13. If E is true whenever F is true, and F is false, what can you conclude about E?

E must be true

E must be false

E could be true or false

E must equal F

E true whenever F is true means F → E. If F is false, the conditional tells us nothing about E.

Explanation

E true whenever F is true means F → E. If F is false, the conditional tells us nothing about E.

14. Which scenario satisfies 'If A or B, then not C'?

A true, B false, C true

A true, B false, C false

A false, B false, C false

A false, B false, C true

The rule (A ∨ B) → ¬C is satisfied when the consequent (¬C) is true or the antecedent is false. Option (b) has antecedent false, so the rule holds.

Explanation

The rule (A ∨ B) → ¬C is satisfied when the consequent (¬C) is true or the antecedent is false. Option (b) has antecedent false, so the rule holds.

15. If W is necessary and sufficient for Z, which statement is false?

If W then Z

If Z then W

If not W then not Z

If not Z then W

W necessary and sufficient for Z means W ↔ Z (biconditional). This gives W → Z and Z → W, but not (¬Z → W).

Explanation

W necessary and sufficient for Z means W ↔ Z (biconditional). This gives W → Z and Z → W, but not (¬Z → W).

LSAT Analytical Reasoning Conditional Logic Rules Quiz

1. If P then Q. If Q then R. What can you conclude if P is true?

2.

What first name or nickname would you like us to use?

2. The contrapositive of 'If not A then B' is:

3. If X or Y must be true, and X is false, what follows?

4. If not S is sufficient for T, which statement is equivalent?

5. When is 'If A then B' false?

6. If all M are N, and all N are O, what can you conclude?

7. If P is necessary for Q, which statement is true?

8. If either C or D is selected, but not both, which scenario violates this rule?

9. If G is sufficient for H, and H is sufficient for I, what must be true?

10. The statement 'Not all R are S' is equivalent to:

11. If exactly one of K or L must be true, and K is true, what follows?

12. If no U are V, what is the contrapositive?

13. If E is true whenever F is true, and F is false, what can you conclude about E?

14. Which scenario satisfies 'If A or B, then not C'?

15. If W is necessary and sufficient for Z, which statement is false?