Hi I am learning group theory and encountered this: $$(B\cap (A\cap B)')\cup (B'\cap (A\cap B)) = B\cap (A'\cup B').$$
I don't understand how this is true, could someone please show me proof?
Thanks
Hi I am learning group theory and encountered this: $$(B\cap (A\cap B)')\cup (B'\cap (A\cap B)) = B\cap (A'\cup B').$$
I don't understand how this is true, could someone please show me proof?
Thanks
Assuming the prime denotes complementation: The second term on the left, $B'\cap(A\cap B)$, is empty, since $B$ and $B'$ are disjoint. That leaves $B\cap(A\cap B)'$. You can use De Morgan's law $(A\cap B)'=A'\cup B'$ to transform this into the right-hand side.