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