Question

For all integers a and b, if a | b then a² | b²?
1) True
2) False

Answer 1

No, the statement 'If a | b then a² | b²' is false.

Step-by-step explanation:

No, the statement 'If a | b then a² | b²' is false. Just because a is a divisor of b, it does not mean that a² is a divisor of b².Let's consider a counterexample where a = 2 and b = 4. Here, a is a divisor of b since 2 divides evenly into 4. However, a² (2² = 4) does not divide evenly into b² (4² = 16).So, the correct answer is 2) False.