Conditional Statements

Read, rewrite, and evaluate if-then statements.

Lesson 2 of 53 parts Practice Flashcards

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Hypothesis and Conclusion

Objective: Identify the hypothesis and conclusion of a conditional.

A conditional has form “If p, then q.” The hypothesis p states the condition; the conclusion q states what follows. A conditional is false only when p is true and q is false.

The region for hypothesis p sits completely inside the region for conclusion q.

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Hypothesis and Conclusion

Objective: Identify the hypothesis and conclusion of a conditional.

A conditional has form “If p, then q.” The hypothesis p states the condition; the conclusion q states what follows. A conditional is false only when p is true and q is false.

Converse, Inverse, and Contrapositive

Objective: Construct related statements without confusing their order.

For p → q: converse is q → p; inverse is ¬p → ¬q; contrapositive is ¬q → ¬p. A statement and its contrapositive are logically equivalent.

Biconditionals and Definitions

Objective: Know when an “if and only if” claim holds.

The biconditional p ↔ q is true exactly when both p → q and q → p are true. Definitions often describe necessary and sufficient conditions.

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