Converse

Definition

The converse of a conditional statement reverses the hypothesis and conclusion. If the original statement is 'If P, then Q,' the converse is 'If Q, then P.'

5 Must Know Facts For Your Next Test

1. The truth value of a converse may differ from the original statement.
2. To find the converse, swap the hypothesis and conclusion.
3. Not all converses are logically equivalent to their original statements.
4. Converse statements are key in understanding logical equivalence and implications.
5. In terms of Venn diagrams, switching sets leads to visualizing the converse.

Review Questions

• What is the converse of 'If it rains, then I will bring an umbrella'?
• Is the converse of a true statement always true?
• How do you form a converse from a given conditional statement?

Related terms

ConditionalStatement: A logical statement with an 'if-then' structure (e.g., 'If P, then Q').

Contrapositive:

The contrapositive swaps and negates both parts of a conditional statement (e.g., 'If not Q, then not P').

Inverse:

The inverse negates both parts of a conditional statement without swapping them (e.g., 'If not P, then not Q').