Question

question 4 of 10
the statement \if a, then b\ can best be described as ______.

a. if a is false, then b might be false.

b. if a is false, then b must be false.

c. if a is true, then b might be true.

d. if a is true, then b must be true.

Explanation:

The logical statement "If A, then B" (a conditional statement) means that whenever A is true, B must be true. Let's analyze each option:

• Option A: The truth of A being false doesn't give a definite relation to B's falsity, so this is incorrect.
• Option B: A being false doesn't imply B must be false; the conditional focuses on A being true leading to B, so this is wrong.
• Option C: "If A, then B" is a stronger statement than B "might" be true when A is true; it's a necessary implication, so this is incorrect.
• Option D: By the definition of a conditional statement "If A, then B", when A is true, B must be true.

Answer:

D. If A is true, then B must be true.