Question

For 2-3, a.) Write the converse of each conditional. b.) Determine if the converse is “always true”, “always false”, or if “it depends”. If it depends or if it is always false, give a counterexample that proves it can be, or is false.

2. If two angles are congruent supplementary angles, then they are right angles. 3. If c is negative and a > b, then ac < bc.

Answer 1

2)

p = two angles are congruent supplementary angles

q = they are right angles

q → p : If two angles are right angles, then they are congruent supplementary angles.

This is ALWAYS TRUE

3)

p = c is negative and a > b

q = ac < bc

q → p : If ac < bc, then c is negative and a > b

This is sometimes true...IT DEPENDS

Counterexample: Let a = -1, c = 2, and b = 3, then ac < bc. Since c is not negative, the statement is false.