Question

What does it mean if the hypothesis is true and the conclusion is false, and then what is the truth value of the conditional statement for the following statement: If the measure of angle XYZ is less than 90 degrees, then angle XYZ is acute?

A) The statement is true.
B) The statement is false.
C) The statement is vacuously true.
D) The statement is undetermined.

Answer 1

If the hypothesis is true and the conclusion is false, it means that the conditional statement is false. In the given statement, 'If the measure of angle XYZ is less than 90 degrees, then angle XYZ is acute', the truth value of this conditional statement is false.

Step-by-step explanation:

If the hypothesis is true and the conclusion is false, it means that the conditional statement is false. This is because a conditional statement is only false when the hypothesis is true and the conclusion is false.

In the given statement, 'If the measure of angle XYZ is less than 90 degrees, then angle XYZ is acute', the hypothesis is true if the measure of angle XYZ is less than 90 degrees. However, the conclusion is false if angle XYZ is not acute. Therefore, the truth value of this conditional statement is false.

Keywords: hypothesis, conclusion, conditional statement, truth value, angle XYZ, acute