Question

Write the converse of the following true conditional statement. If the converse is false, write a counterexample.

If x < 20, then x < 30.

A. If x < 30, then x < 20 ; True
B. If x < 30, then x < 20 ; False -Counterexample: x=27 and x < 27.
C. If x > 20, then x > 30 ; False -Counterexample: x=25 and x < 30
D. If x > 30, then x > 20 ; True

Answer 1

The correct answer is:

B. If x < 30, then x < 20 ; False -Counterexample: x=27 and x < 27.

Step-by-step explanation:

The converse is formed by switching the hypothesis and conclusion. The hypothesis is the part coming after "if"; the conclusion comes after "then." This makes the hypothesis x < 20 and the conclusion x < 30. This means the converse would be

If x < 30, then x < 20.

However, if x = 27, which is less than 30, the converse is not true, since 27 is not less than 20.