Let X be an n-element set. Prove that there are 3n ordered pairs (A, B) of subsets of X such that A ⊆ B ⊆ X   I have a problem proving this... Can anyone please prove this for me? Thank you very much.

Q: Let A and B be two sets. Determine which of the following statements are true and which are false.…

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Q: Let A and B be sets. Prove that A U B = An B if and only if A = B

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: State whether the following claim is true and explain why. (a) Claim: For all sets A, B, and C: (A –…

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Q: Q1:Let U = {1, 2, 3, 4, 5},                                   C = {1, 3}   and A and B are non…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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 any sets (subsets of some universal set U). Use the choose-an-element method to…

A: Two sets A and B are said to be equal if the following hold: A⊆BB⊆A To prove identities that…

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Q: ℘(A) ∪ ℘(B) ⊆ ℘(A ∪ B). Is ℘(A) ∪ ℘(B) = ℘(A ∪ B)? Either provide a proof to show that this is true…

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Q: Which of the following statements are true for all sets A, B, and C?

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Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: If P(A₁) > 0 and if A2, A3, A4,... are mutually disjoint sets, show that P(A2 U A3 U ... |A₁) =…

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Q: Consider the following statements about the powersets of sets A and B. Which of them are true? 1.…

A: The true statements are:2456Explanation:

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Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: Prove T = { ... , −56, −42, −28, −14, 0, 14, 28, 42, ... } is a countable set

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Q: (ANB) –C= (A –C)NB.

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Q: VII.1. Describe the set (R × Z) ∩ (Z × R)

A: We have to describe the set (R × Z) ∩ (Z × R).

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: (a) Give a direct proof of the following statement: "Let A and B be sets. If ACB, then AnB = A."

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Q: 2. Prove Lemma: For all sets A, B, and C, A x (BnC) = (A × B)n (A × C)

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Q: Let A and B be the following sets: A = {m€Z|m=a² + 3 for some odd integer a }, B={n€Z|n is divisible…

A: Let, x belongs to A. Then, x = a²+3 for some odd integer a  So, a being odd, we can write a as…

Q: Let A and B be sets. Prove that (A − B) ∩ (B − A) = ∅.

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