Prove or Disprove: if the complement of A is a subset of B then A union B= U
This is as far as I got.
The complement of A is anything that is NOT A.
If everything that is NOT A IS a subset of B then that does NOT necessarily mean that A union B=U.
Let x be an element in the complement of set A.
If x E of the complement of set A, and the complement of A is the subset of B then A also must be the subset of B. Because A is the subset of B then A union B= B it is NOT EQUAL to U. However, the complement of B union B would equal the universe.