What is a converse of a theorem that is an if-then statement? The if part and the then part switch places.

Question

The if part and the then part switch places.

The converse is the same as the original theorem.
The converse is the same as the original theorem.

The converse of a theorem has no relationship to the original theorem.
The converse of a theorem has no relationship to the original theorem.

The two parts are negated by using the word not.

Answer 1

The best description of the converse of an if-then statement (theorem) is: The if part and the then part switch places.

For example, if the original statement is "If \( P \), then \( Q \)" (written as \( P \rightarrow Q \)), the converse would be "If \( Q \), then \( P \)" (written as \( Q \rightarrow P \)).

The other statements you provided do not accurately describe the converse. The converse is not necessarily the same as the original theorem, it does have a relationship (sometimes true, sometimes false), and negating the two parts describes the inverse or contrapositive, not the converse.