Given that .
It is always true that .
So suppose that if then we are done.
If the by the given and we are done.
Therefore
I need to prove that for all sets A and B, if the complement of A is a subset of B then the union of A and B is equal to U, the universal set.
So far, I've come up with this:
Suppose the complement of A is a subset of B and the union of A and B is not equal to U. Let x be part of the union of A and B. By definition of union, x is a part of A or x is a part of B. Here is where I get stuck...what should I do next? Am I on the right track?
Thanks for any help.