4. Suppose that A, B, C are subset of a set U, and recall the definitions of the elementary set operations n, U, ⇒, \, and ()* from Chapter 11, as well as their characterizations. Prove the following statements, following any method that you prefer. (a) A⇒ B=A* UB. (b) (An B)* = A*UB*. (c) If A ⇒ 0=U \ A = A*. (d) A⇒ (B⇒ C) = (An B) ⇒ C.

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Q: Example 5. If A, B and C are three sets and U is the universal set such that n(U) = 1000, n(A) =…

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Q: The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6,…

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Q: 5. Suppose that A = = {0,1} and B = {0}. (a) Write down the elements of AU B. (b) Write down the…

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Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

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Q: What properties in Abstract Algebra are true if a set is a subset of a different set?

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Q: If a universal set contains 250 elements,

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Q: a) State the intersecton of an indexed family of sets.

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Q: 5. Give an example of a collection (A,, of sets with the properties that: (a) A, # Ø for each i> 1,…

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Q: come up with a (VERY) brief description of the set {2, 4, 6, 8} using set-builder notation.

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Q: Let U be a universal set and A, B, C CU. ITEM 1. Prove: A n BCAUB

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Q: (A – B) – C = A- (BUC)

A: Introduction :

Q: Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B…

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A: (A∩B)={a,b,c,d,e,h}B−A={b,c}(B−C)∪A={b,c,e,g,d,a,f}Explanation:

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