# Thread: how is this possible without using example....by proving

1. ## how is this possible without using example....by proving

1.)If a|bc then a|c
let a = 2 and b = 5 and c = 20

so (5)(20) / 2 = 50
then 20/2 = 10

what if we let a = 3 b= 7 c = 4
(7)(4)/3 = 28/3 = has a remainder... will this be considered true?

2.)if a|c and b|c then ab|c

let a = 2 and b = 5 and c = 20
so 20/2 = 10 and 20/5 = 4 then 20/(2)(5) = 20/10 = 2

what if we let a = 3 b= 7 c = 4
4/3 = 2 and 4/7 = has remainder... will this be considered true?

2. ## Re: how is this possible without using example....by proving

1) is untrue

consider $a=3, c=2, b=6$

$a | 12$ but $a \not | 2$

2) is untrue

consider $a=3, b=6, c=12$

$3 | 12,~6|12,~18 \not | 12$

3. ## Re: how is this possible without using example....by proving

It's not true.

a = 9, b = 3 and c = 6 is a counterexample.