Geometry - Pd ____ Converse, Inverse & Contrapositive Logic

Name ______Date ______

For Conditionals where p → q:

- Converse - you switch the order, so you get q → p

- Inverse - you negate the original, so you get ~p → ~q

- Contrapositive - you switch AND negate the original, so you get ~q → ~p

The original and the contrapositive are LOGICALLY EQUIVILANT (always the same truth value)

The only time a conditional is FALSE is when T → F.

1. Write in symbolic form, the converse 6. Which is logically equivalent to q → ~p

of r → t. (1) ~q →p (3) q → ~p

(2) q → p (4) ~q → ~p

______

2. Write in symbolic form, the inverse 7. If p → q is true, then ~q → ~p is

of q → t. (1) sometimes true (3) always true

(2) never true (4) truth value

______cannot be determined

8. Write out in words, the converse of

3. Write in symbolic form, the inverse "If it's raining, then it's cloudy".

of q → ~p.

______

4. Write in symbolic form the contrapositive 9. Write out the words the contrapositive of

of q → p. "If I passed the Math A exam, then I

achieved a grade of 65% or better."

______

5. Which statement represents the inverse

of the statement, "If I do not practice, 10. If a conditional sentence is true, then its

then I will lose the game"? converse must also be true. (Yes or No)

(1) If I practice, then I will not lose the game. ______

(2) If I lose the game, then I did not practice.

(3) If I practice, then I will lose the game. 11. Which is logically equivalent to p → ~q

(4) If I do not lose the game, then I did practice. (1) ~q → p (3) q → ~p

(2) ~q → ~p (4) ~p → q