IfThen StatementsConverses Section 2 1 Ifthen statement n

If-Then Statements/Converses Section 2 -1

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

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

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

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

Biconditional Statement n n n 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 n n 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 n If you are a ninja, then you are stealthy.