Can anyone help me with these proofs:
1. Prove that for any set A and B, the
where P(X) = power set of X.
2. Prove that for every real number x, there is a real number y such that
3. Suppose F and G are nonempty family of sets and every element of F is disjoint from some element of G. Prove that the union of all sets in F and the intersection of all sets in G are disjoint.
THANKS! MY MATH 109 GRADE DEPENDS ON THIS!