If-Then Statements/Converses

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Presentation transcript:

If-Then Statements/Converses Section 2-1

If-then statement (conditional statement) – has a condition containing a hypothesis and a conclusion. If ________________ then _______________. hypothesis conclusion

Hypothesis / Conclusion The part following the “if” – this part describes the condition necessary to have a desired conclusion. conclusion the outcome when the hypothesis is present – the part following the “then”

Converse the converse of a conditional is found by the and If p, then q – original If q, then p – converse switching hypothesis conclusion

Counterexample an example that shows a conditional statement false. Just one example proves the whole thing to be false.

Biconditional Statement When a statement and its converse are combined using “if and only if” From previous if p then q: P if and only if q is the biconditional iff – represents if and only iff.

From chapter 6 Inverse – if not p, then not q Contrapositive – if not q, then not p

Example Statement If it is a stone, then it is heavy. Converse If it is heavy, then it is a stone. Inverse If it is not a stone, then it is not heavy. Contrapositive If it is not heavy, then it is not a stone. Biconditional It is heavy if and only if it is a stone.

Example 2 If you are a ninja, then you are stealthy.