If ab and cd prove that ac bdSolutionGiven that ab then amb

Solution

Given that a|b then a=mb............(1)

and c| d then c= nd

where m and n are non-zero integer

Now to prove that ac|bd

so its suffies to show that ac= kbd

Now using left side ac and on putting the value of a and c so

ac=(mb)(nd)

=mn(bd)

since m and n are non zero integer so mn is also integer so let k=mn

hence we can write ac=kbd

so ac| bd