# Math Help - True or False hurting my head!!

1. ## True or False hurting my head!!

Hi all,

True or False

If ab Ξ 0 (mod 12) then a Ξ 0 (mod 12) or b Ξ 0 (mod 12). Explain your answer.

I have nothing. lol.

2. I think it's false. As a counter example, take a=2 and b=6. Clearly ab is congruent to 0 modulo 12, but neither a or b is congruent to 0 modulo 12.

3. False.

Counterexample: 4*3 Ξ (mod 12) but neither 4 nor 3 is congruent to 0 mod 12.

4. Let a=14 and b=18, then ab=252 $\equiv$0 mod 12 but is either a or b $\equiv$0 mod 12

5. Thanks Guys.

I can use all of your examples to illustrate that this is incorrect.

Cheers