Write up a formal proof of the following: Claim: For any set A. A C A

Consider the following statement. If U denotes a universal set, then UC = 0. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Let U be a universal set and suppose UC + Ø. So, by definition of complement x EU. Thus x EU and x € U, which is a contradiction. Then there exists an element x in UC. But, by definition of a universal set, U contains all elements under discussion, and so x E U. Let U be a universal set and suppose UC - 0. So, by definition of complement x ¢ U. But, by definition of a universal set, UC contains no elements. Proof by contradiction: Select-- 2 Select- Select 4. --Select- 5. -Select 6. Hence the supposition is false, and so UC = 0. Need Help? Read It

Could you write a formal proof for the following:  For all sets A, B, and C, if A ⊆ B and B ∩ C = ∅ then A ∩ C = ∅.

Let A, B, and C be sets in a universal set U. We are given n(U) = 88, n(A) = 47, n(B) = 42, n(C) = 50, n(A ∩ B) = 26, n(A ∩ C) = 23, n(B ∩ C) = 23, n(A ∩ B ∩ CC) = 15. Find the following values. (a)    n((A ∪ B ∪ C)C)(b)    n(AC ∩ BC ∩ C)