Given the following relation on sets : R={(x,y)1x is a proper subset of y}. Which properties hold for R ? a. Reflexive b. Symmetric C. Antisymmetric d. Transitive Оа. conly b. b, c, d only O C. donly O d. bonly Ое сdonly

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

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Q: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: Assume that A, B, C and D are sets. Verify that (A x B) U (C x D) ≤ (AUC) x (BUD).

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Q: d) The set E = (-1,0) U (0, 1] is an open set. %3D

A: Given set is E = (-1, 0) ∪ (0, 1]

Q: (2b) Let A and B be sets. Prove that A – B is disjoint from A n BC LA O BE

A: The set A∩B is defined as A∩B=x|x∈A and x∈B The set A-B is defined as A-B=x|x∈A and x∉B Two sets are…

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: >) Recall that the symmetric difference of two sets X and Y, denoted XAY = (X-Y)U(Y-X), is the set…

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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: (a) Construct a Venn diagram that expresses the meaning of AAB. (b) Соmpare АДB to BAA. 2. UNION,…

A: Consider two sets A and B, the symmetric difference between the two sets can be given as,…

Q: Let R = {x € Z | x is divisible by 2}. Determine which of the following sets are subsets of R.…

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Q: For the universal set U {a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y,…

A: Solution:     U – { a, b, c, d, e, f, g, h, i ,j ,k ,l ,m ,n ,o ,p ,q ,r ,s ,t ,u ,v ,w ,x , y, z }…

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

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Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

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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: U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A= {2, 3, 5, 8} B = {1, 3, 5, 7, 9} C = {3, 5} D is a set containing…

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

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Q: 1. Use set identities to show that (A U B) n (B U A) = A where A and B are sets. Let A = {1,2, 3}…

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Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

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Q: Let A = {1,2,3} and B = {1,2,3, 4}. The relations R1 = {(1,1), (2,2), (3,3)} and R2 = {(1,1), (1,2),…

A: Given that  R1={(1,1),(2,2),(3,3)}R2={(1,1),(1,2),(1,3),(1,4)} We need to find  a. R1∪R2b. R1∩R2c.…

Q: The difference of two sets, A - B, is defined as the set containing all elements of A except those…

A: U={1,2,3,4,5,6,7,8,9} A={3,5,9} B={2,4,6,7,8,9} A-B=A∩B' Therefore, first find B'=?

Q: 11. For sets A and B, define AAB=(A\B) U (B\A). (a) Let A and B be sets. Prove that A = B if and…

A: For sets  A and B , define                             A∆B=(A \ B)∪(B \ A) .  Then we have to show…

Q: Let A = {0, 1, 2} and let B = {-2, 0, 1, 2}. %3D

A: Given,        A=0, 1, 2, and B=-2, 0, 1, 2

Q: Q1. Let U = {x: x e Z, 3 < x < 15} be the universal set, A = {x: x e U and 2 < x – 3 < 6}, %3D %3D B…

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