1. If we know that |A|<|B| and that A∪B=B, what can we say about the relationship between A and B? 2. Given a set Q = {1,2,3,4,5} and a set P = {2,4,6,8,10} (a) What is P ∩Q? (b) What is P ∪Q? (c) Formally generalize Q: (In other words, how might we describe the contents of Q just using the symbols that we have learned?) (d) Formally generalize P: (In other words, how might we describe the contents of Q just using the symbols that we have learned?)

Q: D. Let A, B, and C be subsets of some universal set U (a) If ANBC C and A° N B C C, prove that B CC

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Q: Find an orthogonal set with the same span (and same number of elements) as 7 -5 4 4 7 (198) -10 -8…

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Q: For two sets A and B, if A=B, then (i) A and B have the same elements (ii) ACB and BCA (iii) x €…

A: Here we have to find the properties of two sets A and B is A= B.

Q: How would you write a formal proof for if AnB = B then B is a subset of A?

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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: Use an element argument to prove the following statement.. Proof: For all sets A, B, and C, An (B-C)…

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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…

Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: 1. Let A = {a, x, c) and B = {b, x, d}. Write down an element of each of th following sets: (a) (An…

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Q: 18 Let U={1,2,3,4,9}, A={2,3}, and B={4,9}. In each of the following questions, find the indicated…

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Q: U={1, 2, 3, 4, 5

A: *Note: As per policy only first three parts are answered. Given: U={1, 2, 3, 4, 5, 6}​, A={3, 4,…

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

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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: (3) Use an element proof to prove that for all sets A, B, C, and D, if An C =0 then (A x B)n (C x D)…

A: The proof of the given statement is given in the explanation part.Explanation:Steps and explanations…

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:

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

A: Consider the given sets:

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: Prove that the following 2 sets are equal: {4k + 5 : k ∈ Z} = {4k + 1 : k ∈ Z}.

A: Two sets are equal if and only if They have the same element  We are using here if x €A. &lt;=&gt;…

Q: 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: 1. Let A = {−30, -10, 10, 30, 50} and B = {-20, -10,0, 10} be subsets of the universal set ε = {10x:…

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Q: (ANB) –C= (A –C)NB.

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Q: Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 32, n(B) = 33, n(C) =…

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