If A and B are any two sets and A U B = A ∩ B, then a. A= Ø b. B= Ø c. A=B d. None of these

Q: (a). If S1,, Sn are open sets in C, then so is Sk. =D1

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Q: Suppose that A, B, and C are sets. Prove that if AC B, then AnC C BN C. Disprove that if An C CBn C,…

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Q: If A,B and C are sets, then (AUB)-C= (A – C)U(B –C). %3D |

A: 14. Given three sets A, B and C. We have to prove that A∪B-C=A-C∪B-C. In order to prove that 2 sets…

Q: Prove: If A,B and C are sets, then A ×(B ∪C) = (A ×B)∪(A ×C).

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Q: If A and B are sets, and A = B, then A and B cannot be disjoint. True False

A: Given that If A and B are sets and A=B then A and B cannot be disjoint.

Q: 2. Find sets A, B, C, D such that the sets (An B) U (C\ D), ((An B)U C) \ D, An(BU C) \ D, An(BU (C\…

A: Example of such set A,B,C,D are given below

Q: For all sets A, B, and C, it holds that (An C) U (B \ C) = (B U C) \ (C \ A). True False

A: We have solve the set true and false

Q: 1. If A and B are sets, show that AB if and only if AUB=B. 2. If A and B are sets, show that AB if…

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Q: (1) *, Let A and B be sets prove the following. (c) A C B if and only if B° C A°.

A: Let A and B be sets.

Q: (3) For sets A, B, and C in some universal set U, prove or disprove the following. (a) AnC = B nc =…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 2. Suppose A, B, and C are sets. Prove that (AUB) \C CAU (B \ C).

A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

Q: If A, B,C, and D are sets, does it follow that (A ⊕ B) ⊕ (C ⊕ D) = (A ⊕ C) ⊕ (B ⊕ D)?

A: The symmetric difference between the set is associative and commutative. So, (A⊕B) ⊕C=A⊕(B⊕C)…

Q: When A, B, and C are sets, A∩(B⋃C) = (A∩B)⋃C if and only if     A ∩ C ⊆ A ∩ B     C ⊆ A     A…

A: According to the given information it is required to tell that when the below statement holds.

Q: If A and Bare any two sets and AUB = ANB, then A = ¢ None of these O Option 1 O Option 4 A = B B = ¢…

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Q: Show that if A and B are sets with AS B, then a) A UB-B. b) ANB-A.

A: Let A and B are two sets with A⊆B a) Let x∈A∪B which implies that x∈A or x∈B. Hence we can imply…

Q: For any sets A and B, which statement is false? OA NA = {} OAUB CANB OAN BC B OA CAUB

A: Remark:  We know that The union of two sets A and B is the set of all those elements which are…

Q: Given the following universal set U={x|x is a letter in "THE FRANCIS MARION UNIVERSITY PATRIOTS"}…

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Q: If A and B are sets such that A C B then A × BC B × B. O true false

A: True.

Q: Let C and D be subsets of a universal set U, then (C ∪ D) ⊆ (C ∩ D).

A: Given C and D are two subsets of universal set U.

Q: (а) An B 3 o (Ъ) в СА (с) АДВ — AU B.

A: The detailed solution is as follows below:

Q: If A C C and B C D then A U BC CU D.

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Q: Show that if A, B, and C are sets, then|A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |A ∩ C| − |B ∩ C| +…

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Q: Given some set A and the universal set U we would say that A u U would result in which of the…

A: Set: A set is a well defined collection of objects. A universal set is a set which contains elements…

Q: Let A, B, and C be non-empty sets. Then A×B×C=A×C×B if and only if

A: A, B, C are three non empty sets,  And, it is given that A × B × C = A × C × B

Q: 9. Let A, B, C and D be any sets. Prove the following: (a) If A CB and BCC, then ACC. (b) If ACC and…

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Q: For all sets D, E and F, if D- FCE-F then DUF CEUF.

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Q: If A and B are sets, then A n (B – A) = Ø. %3D

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Q: For any two sets A and B, if m* (A) = 0, then m* (AUB) = m* (B). In particular, if BCA, then m* (B)…

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Q: If A, B, and C are sets such that A ∩ B ≠ Ø and B ∩ C ≠ Ø, then A ∩ C ≠ Ø

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Q: or any of the sets id, bic it a,bsCthen a b anteo

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Q: If A and B are any two sets and AUB = . A n B, then

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Q: If A and B are sets and A is a subset of B, then A and B cannot be disjoint.

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Q: If S and T are two sets such that S has 21 elements, T has 32 elements, and   S ∩ T has 11 elements,…

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Q: Let A, B, and C be any sets. Mark the statement that is false O A U (BUC) (AUB) UC OACUCC (An C)c OB…

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Q: Let A, B and C be any three sets. Then Ax (BUC)=

A: Given that A, B and C are three sets. We need to find A×{B ∪ C}.

Q: Can you conclude that A = B if A, B, and C are sets such thata) A ∪ C = B ∪ C? b) A ∩ C = B ∩ C?c) A…

A: According to the given information, it is required to conclude that A = B if A,B,C are sets such…

Q: If A and B are sets, then P(A) U P(B) = P(A U B). Select one: o True o False

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Q: 30. Given A, B,C, and D are sets, if ACB and CcD, then A×CcBxD. T. b c e

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Q: If A and Bare any two sets and AU B = ANB, then B = ¢ None of these O Option 2 Option 4 A = 6 A = B…

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Q: Show that if A and B are sets |A| = |B|, then |P(A)| = |P(B)|

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Q: for any sets A and B (AUB)'=A'nB'

A: We prove that for any sets A and B (AUB)'=A'nB'.

Q: 2. If A, B and C are sets, use a membership table to prove or disprove: A U (B N c) = (A U B) n (A U…

A: First we prove that left hand side is subset of right hand side and then right hand side is subset…

Q: Given a set A of n elements, in how many ways can you find two set P,Q ⊆ A (not necessarily…

A: Given set of  elements we need to find number ways in which A can be written as union of two…

Q: Let A, B, and C be non-empty sets. Then C×B×A=C×A×B if and only if * O None of these O A=C B=C A=B=C…

A: Given :- A, B and C are three non empty sets. To complete the statement. C*B*A = C*A*B if and only…

Q: Let A and B be sets. Then B - (B – A) AN B is equal to the above

A: Let A and B be sets  Let x∈B-B-A ⇔x∈B and x∉B-A ⇔x∈B∧x∉B∨x∈A⇔x∈B∧x∉B∨x∈B∧x∈A⇔x∈B∧x∈A⇔x∈A∩B ( since…

Q: If A,B and C are sets, then A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

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Q: If 'U' is universal set and 'Ø' is null set then, which of the following is correct option, (a) UUØ…

A: We have to perform various operations as indicated in the four options in the given question.  a) U…

Q: 31. If A and B are sets and An B = A, then ОВСА O B is empty O AC B A and B are

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Q: Let A, B,C be three sets. Show that if BC A and CCA\B, then BC A\C.

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Q: If A,B and C are sets, then (AUB)-C=(A-C)U(B–C).

A: