1.3Converse, Inverse, and Contrapositive
Quick Answer
Given "If p, then q": Converse: If q, then p. Inverse: If ¬p, then ¬q. Contrapositive: If ¬q, then ¬p. A conditional and its contrapositive are logically equivalent; the converse and inverse are logically equivalent to each other.
Essential Question
How do the converse, inverse, and contrapositive relate to the original conditional, and which pairs are logically equivalent?
Learning Goals
- 1Write the converse, inverse, and contrapositive of a conditional.
- 2Determine the truth value of each related conditional.
- 3Identify logically equivalent statements.
- 4Write biconditional statements.
Key Vocabulary
Converse
Switches the hypothesis and conclusion: If q, then p.
Inverse
Negates both parts: If ¬p, then ¬q.
Contrapositive
Switches and negates both parts: If ¬q, then ¬p.
Logically equivalent
Two statements that always have the same truth value.
Biconditional
A statement of the form "p if and only if q" (p ↔ q); true when p and q have the same truth value.
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.