Logic and conditionals

Objective

Analyze conditional statements and their converse, inverse, and contrapositive.

What it means

A conditional statement has the form 'If p, then q.' The hypothesis p is the condition, and the conclusion q is the result.

Key terms

Conditional

A statement of the form 'If p, then q.'

Converse

Swaps hypothesis and conclusion: 'If q, then p.'

Inverse

Negates both parts: 'If not p, then not q.'

Contrapositive

Swaps and negates both parts: 'If not q, then not p.'

Rules to remember

• A conditional and its contrapositive always share the same truth value.
• A converse and an inverse always share the same truth value.
• A biconditional ('p if and only if q') is true only when the conditional and converse are both true.

Step by step

1. 1Identify p and qFind the hypothesis (p) and conclusion (q) in the original statement.
2. 2Apply the transformationSwap and/or negate p and q depending on which form is asked for.
3. 3Write the new statementRebuild the 'If ..., then ...' sentence with the new parts.