Assume that:
This means that:
If we call m and n then we can rearrange them to get:
Now, we expand yet again:
If x is in the intersection of the two, then they both have x in common, which means that:
This is sufficient to prove that:
Let A, B, C be sets..
Prove that (AUB)∩ C is contained in AU(B∩ C)
I know how to show this using the venn diagram, and one professor I had told us just drawing the venn diagram is proof enough, but I think this professor wants a more formal proof.
My idea is to maybe let x belong to (AUB)∩ C and then this is like (A∩ C)U(B∩ C) and then A∩ C contains AU(B∩ C), but I feel like I am just running in circles.
Thanks for any help.