Question

For any natural numbers (a), (b), and (c), assume (a | b) and (a | c). Which of the following statements is not necessarily true?

a) (a | (b + c))
b) (a | (b - c))
c) (a | (2b))
d) (a | (bc))

Answer 1

The statement that is not necessarily true is (a | (b - c)).

Step-by-step explanation:

The statement that is not necessarily true is (a | (b - c)).

For (a | b) and (a | c) to be true, it means that a is a divisor of both b and c.

However, (a | (b - c)) does not necessarily hold true. For example, let's say a = 2, b = 9, and c = 5. (2 | 9) is true because 2 is a divisor of 9. Similarly, (2 | 5) is true because 2 is a divisor of 5. But (2 | (9 - 5)) is not true because 2 is not a divisor of 4.