1. Let A be a nonempty collection of sets. Determine the truth of each of the following statements and of their converses: (a) x e UAE4 A = x € A for at least one A e A. (b) x €UAEA A = x € A for every A e A. (c) x ENAEA A = x € A for at least one A E A. (d) x €NAEA A = x € A for every A e A.

Q: Let A, B and C be sets . The proof of (AU (BNC) C AN (BU c) is as follows: Let x E ( Αυ (ΒηC) x E Ā…

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Q: O ACBiff P(A) C P(B). O ACBIF and only if AU B= B (A x B) U (C x D) (AUC) x (BU D)

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Q: 5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In…

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Q: . If A and B are sets in a universal set U, then AUB=AnB. A-(BnC)=(A-B)U(A-C). . If A, B and C are…

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Q: P(A) denote the powerset of a set A. Write the following sets by listing their elements between…

A: We have to find out all the elements in given set.

Q: Given a universal set U for a set X , if AC X , then (U – X) n A = Ø

A: Given a universal set U for a set X and A⊆X We shall prove it by contradiction method. Let us assume…

Q: (a) An (B-C)= (A-C) nB (b) A (B-C) = (A - B) - C (c) (A-B) U (B-A) = (ANB) (d) (A-B)U(B-A) = AUB (e)…

A: Given that A, B and C be sets

Q: Which of the following is true for all sets S and T? Select one: O A. SOT SOT B. SOT SUT C. SUT SOT…

A: see below the answer and explanation

Q: iii. Is the set compact in ²? {(a₁, a2, a3, ...) € l² : |an| ≤ = } and <==}

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Q: O (A x B) U (C x D) C (AUC) x (BUD)

A: Please check step 2 for the solution.!

Q: (4) Prove by contradiction, for any sets A and B, if ACA- B, then An B= Ø

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Q: Determine if the following statements are true or false. Here A represents any set. (a) oCA (b) A'CA…

A: Here let us consider A to be any set which consists some elements U is a universal set  A' is a…

Q: Find conditions on sets A and B as subsets of R to make each of the following statements true. a.…

A: The objective of the question is to find the conditions on sets A and B that would make the given…

Q: Let A = {Ba:a € A} be a family of sets and let G be a nonempty set. Prove U B.) = U(Gn B.) Order…

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Q: Is the set {(a₁, A2, A3, ...) € l² : |an| ≤ compact in 2? √n

A: As per the question we are given a set consisting of the infinite sequence : (a1 , a2 , a3 , ..., )…

Q: Let (5,}nen is a disjoint segeuence of measurable sets , then: H(S) ulgn

A: Ans : true , because

Q: (a) If ANC C Bn C, then A C B. (b) If A U C C BUC, then A C B. (c) If A U C = BU C, then A = B.

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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: VI. De-Morgan's Laws : If A, B and C are any two sets, then (i) (A U B) = A'O B' (ii) (An B) = A'U…

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Q: Let A = {Ba:a € A} be a family of sets and let G be a nonempty set. Prove GnU B.) = U(GN B.) Order…

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set A × B = {(a, b) : a E…

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Q: For any set S if a*b = b*a, Va, b e S then * is said to be on S. (A) closed (B) associative (C)…

A: (a) For any set S if a*b∈S , ∀a, b ∈S , then *is closed on S   (b) For any set S if a*(b*c) =…

Q: Suppose that A and B are sets such that AC B. Which of the following must be true? Select all that…

A: The question is asking us to determine which of the given statements must be true if set A is a…

Q: Let S and T be sets. Identify all of the following statements that are equivalent to the statement…

A: Let S and T be sets and T⊆S. Now, T⊆S , which means set T is a subset of set S. A collection of…

Q: Find conditions on sets A and B as subsets of R to make each of the following statements true. a.…

A: The objective of the question is to find the conditions on sets A and B that would make the given…

Q: Let the universal set be the set R , and let A={xER| 0≤ x <4 } B= {XER| 2<x≤10} Find  a. B-A  b.…

A: Given A= { x ∈R :0≤ x &lt;4 }, B= {X∈R : 2&lt;x≤10} Given universal set be the set R.

Q: et the domain be the set of all people. Let: P(x, y): x knows y. Vhich of the following is the…

A: Here we use predicate logic

Q: IV. Associative Laws : If A, B and C are any three sets, then (1) (A U B) U C = AU (BUC) (ii)…

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Q: Let A, B and C all be sets with a universal set U. Prove or disprove the following statements: i. If…

A: Let's prove or disprove each statement:i. If B⊆C then (A×B)⊆(A×C):Proof:Assume B⊆C. Let (x,y) be an…

Q: et X, Y , and Z be sets. (a) Construct examples for X, Y and Z so that the following conditions are…

A: Open set:  if A°= A then set 'A' is said to be                    open set. Where, A° is set of all…

Q: V Let A. B be sets Prove that AnB = if and only if A B

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Q: Show that the closure operation has the following properties: (a) If E1 CE2, then E1 CE2. (b)…

A: According to the guidelines I am going to solve the first three subparts of the problem, please post…