To solve the problem of identifying the converse of a given conditional statement [tex]\( p \rightarrow q \)[/tex], let's follow these steps:
1. Understand the conditional statement [tex]\( p \rightarrow q \)[/tex]:
- Here, [tex]\( p \)[/tex] is the hypothesis or antecedent.
- [tex]\( q \)[/tex] is the conclusion or consequent.
- The statement reads as "If [tex]\( p \)[/tex], then [tex]\( q \)[/tex]."
2. Define the converse of [tex]\( p \rightarrow q \)[/tex]:
- The converse of a conditional statement [tex]\( p \rightarrow q \)[/tex] is obtained by reversing the hypothesis and conclusion.
- Thus, the converse is [tex]\( q \rightarrow p \)[/tex].
- The converse reads as "If [tex]\( q \)[/tex], then [tex]\( p \)[/tex]."
3. Examine the given options to identify which one represents the converse:
- Option 1: [tex]\( \sim p \rightarrow \sim q \)[/tex]
- This means "If not [tex]\( p \)[/tex], then not [tex]\( q \)[/tex]."
- This is actually the inverse of the original statement, not the converse.
- Option 2: [tex]\( - q \rightarrow - p \)[/tex]
- This notation seems to be another way to denote the inverse. However, it's unusual and not standard.
- Option 3: [tex]\( q \rightarrow p \)[/tex]
- This is the direct form of the converse. It means "If [tex]\( q \)[/tex], then [tex]\( p \)[/tex]", which matches our definition of the converse.
- Option 4: [tex]\( p \rightarrow q \)[/tex]
- This is the original conditional statement itself and not the converse.
4. Conclusion:
- Based on our reasoning, the correct option that represents the converse of [tex]\( p \rightarrow q \)[/tex] is [tex]\( q \rightarrow p \)[/tex].
- Thus, the answer is: [tex]\(\boxed{3}\)[/tex].
