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

The correct answer is:

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

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.

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