1. Contrapositive and Inverse
Section 2 ½
(NIB)

2. 1) If I play Monopoly, then I throw dice
1) If I play Monopoly, then I throw dice. (original) 2) If I throw dice, then I play Monopoly. (converse)
Euler Diagrams: 1) 2) Note: If a point is not inside larger circle, then it is not inside smaller circle. 1) If I play Monopoly, then I throw dice. 3) If I do not throw dice, then I do not play Monopoly. (Note: this statement is called the contrapositive of #1)

3. Contrapositive: statement formed by interchanging the hypothesis and conclusion and denying both.
Symbolically: a  b (conditional statement)
not b  not a (contrapositive)
Since both are represented by the same Euler diagram, they are logically equivalent (both true or both false)
1) If I play Monopoly, then I throw dice. (original)
2) If I throw dice, then I play Monopoly. (converse of #1)
4) If I do not play Monopoly, then I do not throw dice.
(contrapositive of #2 and inverse of #1)

4. Inverse: statement formed by denying both the hypothesis and conclusion.
Symbolically: a  b (conditional statement)
not a  not b (inverse)

5. 1) If I play Monopoly, then I throw dice. (original)
2) If I throw dice, then I play Monopoly. (converse)
3) If I do not throw dice, then I do not play Monopoly. (contrap)
4) If I do not play Monopoly, then I do not throw dice. (inverse)
(also the contrapositive of the converse)
Since the converse and the inverse are both represented by the same Euler diagram, they are logically equivalent
(both are true of both are false)

6. Summary: Logically equivalent: Conditional statement: a  b
Contrapositive: not b  not a
Converse: b  a
Inverse: not a  not b

7. Example 1: If you are old then you are wise. Write the following:
a) Converse:
b) Contrapositive:
c) Inverse:
If you are wise, then you are old.
If you are not wise, then you are not old.
If you are not old, then you are not wise.

8. Homework:
Read notes
Do worksheet #1 - 40