Determine whether each of the following is true or false. If true, prove the statement. If false, find a counterexample.

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Determine whether each of the following is true or false. If true, prove the statement. If false, find a counterexample.

a) For all integers a, b,and c, if a | b and a | c then a | (3b − 5c).

b) For all integers a ≥ 4 and b, if a | 3b then a | b.

EXPERT ANSWER

1) suppose a|b and a|c then a|3b and a|5c

=>a|3b and a|-5c

Thus ‘a’ divides their sum

=>a|3b-5c

2)this is not true let a=6 and b=4

Then 6|3×4 but a=6 does not divide b=4