Prove for all sets of A, B, that P(A) U P(B) is a subset of P(AUB).

Q: Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

A: (d) Let, x ∈ (A')'       => x ∉ A'       => x ∈ A      So, (A')' ⊆ A. . . . . . (I)…

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let A…

Q: How do I write a set T such that S is an element of T and a proper subset of T?

A:

Q: Let A, B, and C be sets. Prove (AUB)NC= (ANC) U(BNC)

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Q: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

Q: Let A, B and C be subsets of a universal set U. Prove that (a) ACB if and only if An Bc = Ø. (b) An…

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Q: Prove that the set Q \ Z is countable.

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Q: Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A…

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Q: Let U be the universal set with disjoint subsets A and​ B, where n(U) = 37​, n(A) = 8​, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law  A'∩B' =…

Q: 2. Prove for any sets A, B that (An B) = A if and only if A C B.

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Q: How many subsets are there for the set {h, j}?

A: The given set is {h, j}.It is known that, “If a set contains ‘m’ elements, then the number of…

Q: 2. Find a set A such that A = {2, JA]}.

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Q: (ANB) –C= (A –C)NB.

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Q: Prove that each of the properties in parts (a)–(d) holds whenever A and B are finite sets.a) J(A, A)…

A: Since there are multiple sub parts posted, we will answer first three parts. If you want any…

Q: Construct an example of a subset B of p({a, b, c, d}) such that (B, C) is a totally ordered set.

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Q: Prove A is a subset of (A U B)

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Q: Q.No.2 Let X be a universal set and A, B be the subsets of X.Then prove the following. (a) ((A*…

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Q: Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A…

A: We have given the following n(U) = 300, n(A) = 150, n(B) = 120, and n(A ∩ B) = 60.

Q: Let A1,A2,.......,An be countable sets. Prove that  A1 x A2 x.............An = { a1, a2,…

A: Let A1,A2,.......,An be countable sets. Then we have to show that    A1 x A2 x.............An = {…

Q: Let A = {1, 2, 3} and B = {2,5} be two subsets of a universal set U {1, 2, 3, 4, 5). Compare (AUB)…

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Q: Prove that for every n E N if A is a set with n elements, then the power set of A, P(A), has 2"…

A: The set P(A) contains every possible subset of A, including the empty set and the set A itself.

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.