Exercise 1. Let A, B and C be sets. 1. Verify that AUB BUA 2. Verify that AU(BnC) (AU B)n (AUC) 3. Verify that An (BUC)-(AnB)U(Anc). Exercise 2. Let U be a set. 1. Let A, B be subsets of U. Verify that AnB- AuB. 2. Prove by induction on n N, starting with n-1, that A n n An-A U U An where A, An are subsets of U. (You may use the previous part.) Exercise 3. Prove that for all positive n E N, n2 Exercise 4. Prove that for all positive n e N, 12+22++n2n+), These are pyramid 2 n(n+1)(2n numbers: https://en.wikipedia.org/viki/Square pyramidal number.)