Let R be the equivalence relation on the set A = { a, b, c, d } induced by the partition ({a}; {b, c}; {d}). Select all pairs of elements in R. (a,a) (a,b) (a,c) (a,d) (b.a) (b.b) ☐ (b,c) (b,d) (c.a) ☐ (c,b) (c.c) ☐ (c,d) (d,a) (d,b) (d,c) (d,d)

Q: (24 pts) Either show the following relations are equivalence relations, or show which qualities of…

A: a. S = {0, 1, 2, 3}, R = {(0,0), (1, 1), (1, 2), (2, 1), (2,2), (2, 3), (3, 3)} Reflexive: Yes. We…

Q: Prove: For all sets A, B and C, (AUB) - (CA) = AU (B-C).

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

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Q: Let P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence…

A: P={{a,b,d},{c,f},{e,g}} . The  equivalence relation is as follows:…

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: In the expressions given below, calculate the indefinite integral using the method of integration by…

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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: let A= {a, b, c, d} and R= { (a,a), (a, c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. draw a…

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

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: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

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Q: 3) a) Suppose A = {0,1,2,3,4} and R = {(0,0). (0,4).(1.1), (1,3).(2,2).(3,1).(3,3),(4,0).(4,4)} is…

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Q: Let the universe of elements include these letters: p, q, r, s, t, u, v, w, x, y. The first set A…

A: The universe set contains the elements: p, q, r, s, t, u, v, w, x, y The set A contains the…

Q: For all sets A, B, and C, prove that (AUB) - (CA) = AU (B-C) Please indicate the reason for each of…

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Q: Let A and B be any sets. Show that: (a) A – B, B - A, and An B are disjoint with each other. (b) A =…

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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: (a, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Let A,B,C,D be sets. Prove that (A∩B)×(C∩D)=(A×C)∩(B×D)

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Q: Suppose A, B, C are sets. Prove that (AUB) – C = (A − C) U (B − C)

A: A∪B-C=A-C∪B-C

Q: (ANB) –C= (A –C)NB.

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Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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Q: a and b be disjoint subsets of the universal set U. Assume n(U) = 110, n(A)=50 and n(B) = 25. Find…

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Q: Let U = {1, 2, 3, 4, 5} be the universal set. Let A = {1, 2, 3}, B = {1, 3, 5}, and C = {2, 4, 5}.…

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