To address this question, let’s first review the definitions of different forms related to a conditional statement.
1. Original Conditional Statement:
This statement is typically written as [tex]\( p \rightarrow q \)[/tex], which can be read as "if [tex]\( p \)[/tex], then [tex]\( q \)[/tex]". Here, [tex]\( p \)[/tex] is the hypothesis, and [tex]\( q \)[/tex] is the conclusion.
2. Inverse:
The inverse of a conditional statement [tex]\( p \rightarrow q \)[/tex] is the statement [tex]\( \neg p \rightarrow \neg q \)[/tex], where [tex]\( \neg p \)[/tex] and [tex]\( \neg q \)[/tex] are the negations of [tex]\( p \)[/tex] and [tex]\( q \)[/tex], respectively. This translates to "if not [tex]\( p \)[/tex], then not [tex]\( q \)[/tex]".
3. Converse:
The converse of the conditional statement [tex]\( p \rightarrow q \)[/tex] is obtained by switching the hypothesis and the conclusion, resulting in [tex]\( q \rightarrow p \)[/tex]. This means "if [tex]\( q \)[/tex], then [tex]\( p \)[/tex]".
4. Contrapositive:
The contrapositive of the conditional statement [tex]\( p \rightarrow q \)[/tex] involves both switching the hypothesis and the conclusion and negating both. This results in [tex]\( \neg q \rightarrow \neg p \)[/tex], which means "if not [tex]\( q \)[/tex], then not [tex]\( p \)[/tex]".
Given the statement [tex]\( q \rightarrow p \)[/tex]:
- This form matches the definition of the converse of the original conditional statement [tex]\( p \rightarrow q \)[/tex].
Therefore, the correct identification for the statement [tex]\( q \rightarrow p \)[/tex] is:
The converse of the original conditional statement.
So, the answer is:
3. The converse of the original conditional statement
