2. Contrapositive, Inverse, and Converse
Lesson 2.1

3. Counterexample Consider question 3a on the Do Now.
An EXAMPLE that proves the conjecture is false. (note: a counterexample simply disproves a statement but does NOT prove the converse)

4. Clear Boards OUT! If a number is prime, then it is even
If two angles are acute, then they are congruent

5. Notation Conditional Statement “If p then q” Negation “not p”
Example: if p is “it is raining” then p is “it is not raining
Converse
“If q then p”
Inverse
“If not p then not q”
Contrapositive
“If not q then not p”

6. What is Truth?!?!?!

7. Example 1
Consider the statement: If you live in Newark, then you live in New Jersey
Find:
Converse:
Inverse:
Contrapositive:

8. Analyze each statement. Is it true? What conclusions can we draw?
You Try!
Find the converse, inverse, and contrapositive of each of the following statements.
If a person is 18 years old, then he or she may vote in federal elections.
If angles are right angles then they are congruent
If an angle is a right angle, then it measures 90.
Analyze each statement. Is it true? What conclusions can we draw?

9. If the conditional statement is true, then the contrapositive is true.
If the statement is a definition, then the converse, inverse, and contrapositive are all true. (Definitions are said to be reversible)
If the statement is a theorem, the converse and inverse are not (necessarily) true.