Question 1

What is the logical form of a conditional statement, and what are its two components called?

Accepted Answer

A conditional statement takes the form 'If P, then Q' (P → Q). P is called the sufficient condition (antecedent), and Q is called the necessary condition (consequent).

Question 2

What is the contrapositive of 'If P, then Q,' and why is it logically significant?

Accepted Answer

The contrapositive is 'If not Q, then not P' (¬Q → ¬P). It is logically equivalent to the original statement, meaning it is always true whenever the original is true.

Question 3

What is the inverse of 'If P, then Q,' and is it logically equivalent to the original?

Accepted Answer

The inverse is 'If not P, then not Q' (¬P → ¬Q). It is NOT logically equivalent to the original conditional statement.

Question 4

What is the converse of 'If P, then Q,' and is it logically equivalent to the original?

Accepted Answer

The converse is 'If Q, then P' (Q → P). It is NOT logically equivalent to the original conditional statement.

Question 5

When the phrase 'only if' appears in a sentence, such as 'P only if Q,' how should this be translated into a conditional statement?

Accepted Answer

'P only if Q' translates to 'If P, then Q' (P → Q). 'Only if' introduces the necessary condition, not the sufficient condition.

LSAT Formal Logic Mastery

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