1. If-Then Statements/Converses
Section 2-1

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

3. 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”

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

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

6. 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.

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

8. 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.

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