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If an original conditional statement is represented by [tex]\( p \rightarrow q \)[/tex], which represents the contrapositive?

A. [tex]\( q \rightarrow p \)[/tex]
B. [tex]\( \sim q \rightarrow \sim p \)[/tex]
C. [tex]\( p \rightarrow q \)[/tex]
D. [tex]\( \sim p \rightarrow \sim q \)[/tex]

Sagot :

GinnyAnswer
To understand how to find the contrapositive of a conditional statement, let's start by breaking down the original conditional statement:

1. Original Conditional Statement: [tex]\( p \rightarrow q \)[/tex]

This means "If [tex]\( p \)[/tex], then [tex]\( q \)[/tex]."

To form the contrapositive of a conditional statement ([tex]\( p \rightarrow q \)[/tex]), we need to negate both the hypothesis and the conclusion and reverse the direction of implication.

2. Negate Both Hypothesis and Conclusion:
- The negation of [tex]\( q \)[/tex] is [tex]\( \sim q \)[/tex]
- The negation of [tex]\( p \)[/tex] is [tex]\( \sim p \)[/tex]

3. Reverse Direction:
- So, the contrapositive of [tex]\( p \rightarrow q \)[/tex] becomes [tex]\( \sim q \rightarrow \sim p \)[/tex].

Thus, the contrapositive of the conditional statement [tex]\( p \rightarrow q \)[/tex] is [tex]\( \sim q \rightarrow \sim p \)[/tex].

Therefore, the answer is:
[tex]$\sim q \rightarrow \sim p$[/tex]
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