1

2.5 Converse, Inverse, and Contrapositive 

Conditional #1:  If I live in Allegany, then I live in New York.

Conditional #2:  If two angles have equal measure, then they are congruent.

Conditional in symbolic form:

Converse:

Contrapositive:

Inverse:

switch

negate

switch and negate

2

Construct a truth table for Converse, Inverse, and Contrapositive

p q ~p ~q p q q p ~p ~q ~q ~p

conditional

converse

inverse

contrapositive

�A conditional and its contrapositive are logically equivalent.

3

1) Identify the converse, inverse and contrapositive of the statement:        "If today is Presidents' Day, then there is no school."

1.  If there is school, then today is not Presidents' Day. 2.  If there is no school, then today is Presidents' Day. 3.  If today is Presidents' Day, then there is school. 

   4.  If today is not Presidents' Day, then there is school. 

Try These:

2) Which statement is logically equivalent to ∼a  → b?1.  a → ∼b 2.  b → ∼a 3.  ∼b → a 4.  ∼b → ∼a 

4

Write the converse, inverse, and contrapositive for the following:

3) If I don’t set my alarm, then I’ll be late for school.

Converse:

Inverse:

Contrapositive:

4) t à ~w

Converse:

Inverse:

Contrapositive:

5) ~p à ~q

Converse:

Inverse:

Contrapositive:

5

Homework:

Page 67, 4-6, 8, 9, 15 - 21 odd, 24 - 28