Question $1.$ Consider the statement 'For all integers $a,b$ and $c,$ if $ab|c|$ then $a|c|$ and $b|c|.\text{'}$ Determine whether the statement is true or false. If it is true, prove the statement directly from the definitions. If it is false, give a counterexample.

Question $2.$ Consider the statement 'For all integers $a,b$ and $c,$ if $a|bc|$ then $a|b|$ or $a|c|.\text{'}$