When considering a conditional statement [tex]\( p \rightarrow q \)[/tex], it's important to understand the concept of a contrapositive. The contrapositive of [tex]\( p \rightarrow q \)[/tex] is created by reversing and negating both parts of the statement.
To break it down step-by-step:
1. Identify the components:
- [tex]\( p \rightarrow q \)[/tex] is the original conditional statement, meaning "If [tex]\( p \)[/tex] then [tex]\( q \)[/tex]."
2. Negate both components:
- [tex]\( \sim q \)[/tex] means "not [tex]\( q \)[/tex]."
- [tex]\( \sim p \)[/tex] means "not [tex]\( p \)[/tex]."
3. Reverse the order:
- The parts are swapped.
So, the contrapositive of [tex]\( p \rightarrow q \)[/tex] is [tex]\( \sim q \rightarrow \sim p \)[/tex], which translates to "If not [tex]\( q \)[/tex], then not [tex]\( p \)[/tex]."
Therefore, the correct answer is:
[tex]\[
\boxed{\sim q \rightarrow \sim p}
\][/tex]
