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]
