Question

provide a counterexample (specific values of a,b, etc. which make the statement false) for each of the following statements. Assume that a,b,c,d ∊ ℤ for all statements. 1. If a I bc, then a I b or a I c. 2. If ab I cd , then a I b and c I d. 3. If a I b^2 , then a I b.

Answer 1

1. a=3, b = 2, c = 1.

2. a=2, b=3, c=4, d=6.

3. a = 9, b = 3.

Explanation:

1. 3 | 21 is a counterexample because 3 does not divide into 2 or 1.

2. 23 | 46 is a counterexample because 2 does not divide into 3.

3. 9 | 3^2 is a counterexample because 9 does not divide into 3.