Contrapositive, Inverse, and Converse

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Presentation transcript:

Contrapositive, Inverse, and Converse Lesson 2.1

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)

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

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”

What is Truth?!?!?!

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

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?

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.