relation between union and intersection A and B are any two sets.
if A U B ≠ B
is it also true that A ∩ B ≠ A ?
and if so then why?
This is just a step I am using for a bigger proof, if the above is not true then I'll have to search for a different direction.
Thanks in advance.

If $A\cup B\ne B$, then there is some $a\in A$ such that $a\notin B$, so $a\notin (A\cap B)$, so $A\cap B\ne A$.
