Question

1. which of the following symbolic notations represents the converse of a conditional statement?

a. $p \
ightarrow q$
b. $\sim p \
ightarrow \sim q$
c. $q \
ightarrow p$
d. $\sim q \
ightarrow \sim p$

Explanation:

To determine the converse of a conditional statement, recall that a conditional statement is in the form \( p
ightarrow q \) (where \( p \) is the hypothesis and \( q \) is the conclusion). The converse of a conditional statement switches the hypothesis and the conclusion. So, if the original is \( p
ightarrow q \), the converse is \( q
ightarrow p \).

• Option A: \( p

ightarrow q \) is the original conditional statement, not the converse.

• Option B: \(

eg p
ightarrow
eg q \) is the inverse of the conditional statement (negating both hypothesis and conclusion), not the converse.

• Option C: \( q

ightarrow p \) switches the hypothesis (\( p \)) and conclusion (\( q \)) of the original \( p
ightarrow q \), which is the definition of the converse.

• Option D: \(

eg q
ightarrow
eg p \) is the contrapositive (negating and switching hypothesis and conclusion), not the converse.

Answer:

C. \( q
ightarrow p \)