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

Q: Give examples of sets A, B and C such that: (a) A ∈ B and B ∈ C, and A /∈ C (b) A ∈ B and B ∈ C, and…

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

A: Explanation A and B:

Q: Let 4, B, and C be sets. Show that а) (А — В) — С СA-C. b) (A — C) n (С- В) — 0.

A: It can be solved by the set theory

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: 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: 1. example of sets A and B for which A B but Ag B.

A: Cardinality of a set is number of elements in the set.

Q: Let 4, B, and C be sets. Show that a) (A - B) – CSA C. b) (A - C) n (C- B) = 0.

A: Answer

Q: IF A and B are sets then A-BC A UB

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Q: Prove that if A and B are sets, then P(A) U P (B) C P(AUB).

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Q: Let A, B, and C be sets. Show that (A − B) − C = (A − C) − (B − C).

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Q: Prove : a. For any sets A and B, AXB=BXA b.For any sets A, B, C (A x B) x C Ax B x C AX (BXC) c. If…

A: let the set A and B are A= ( m,n)   , B = (n,m) Now, A×B = {(m,n), (n,n),(n,m),(m,m)} B×A=…

Q: Let A, B be any sets with ACB. Then* |P(B × B)| > |P(Ā × B)| O None of these the above is true |P(A…

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Q: Let A and B be sets. Prove that A c B if and only if A NB = A.

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

A: We can tackle this problem easily by assuming some examples  case (i) Let A=B=C = {1,2} we have,…

Q: If A,B and C are sets, then A x (B-C) = (A × B)- (A x C). |

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Q: Prove if the following statement is true or disprove if it is false. If A and B are finite sets,…

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Q: Let A, B, and C be sets. Prove A × (BnC) = (A × B)n (A × C).

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Q: 1. Let A and B be sets. Prove that A C B if and only if An B=A

A: Prove that A⊂B if and only it A∩B

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

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Q: Let A and be any sets. Mark the statement that is true OAUB CA OA - B C В В СВ O AC = { } = OANB C в

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Q: Suppose A and B are two sets such that ANB = Ø. Which of the following statements is/are true? (i)…

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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: 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: Exercise 3.1.6: Which statements are true for all sets? Which of the following statements are always…

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Q: 2. Let C and D be subsets of a universal set U, then 2, (C ∩ D) ⊆ (C4D).

A: False

Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

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Q: Prove or disprove: For all sets A,B and C: (A-B)-C = A-(BUC).

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Q: Find an example of sets A and B such that |A|=3,|A|=3, |B|=4,|B|=4, and |A∪B|=5.

A: Let A = {2, 3, 4} and |A|= 3 and B = {2, 4, 6, 8} and |B|= 4 The union of set A and B is the set of…

Q: 3. Let A, B, and C be sets. Prove or disprove that A- (BNC) = (A-B) U (A-C).

A: Solution

Q: Assume that the statement applies to all sets. Is it true or false? A – (BO C) = (A – B) (A – C) 2.

A: A-(B INTERSECTION) C= (A-B)INTERSECTION(A-C)

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

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

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Q: If A, B and C are sets such that; A ∆ B = A ∆ C, then   B is a subset of C        Select one: A.…

A: The meaning of A ∆ B is A ∆ B = (A u B) - (A n B) So A ∆ B contains that elements from set A and set…

Q: Let A and B be sets with A ⊆ B and B transitive. Prove each of the following: 1. P(A) ⊆ P(B). 2.…

A: It is given that the set A is a subset of the set B. First we have to show that PA is a subset of PB…

Q: 2. Determine if the following statements are true or false. Here A represents any set. (a) ¢ C A (b)…

A: Used simple logic to prove.

Q: (i) If A and B are two sets such that ACB, then m* (A) ≤m* (B).

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

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Q: Let A B be any Sets then A B ifp PA) e PCB)

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

A: B=C

Q: 3. Let A, B, C, and D be sets. (a) Prove that (A × C) n (B × D) = (An B) × (Cn D).

A: Let A, B, C, and D be sets.To prove the equality, we have to show that, LHS is a subset of RHS and…

Q: Let A and B be sets. Prove that PLA) O P(B) = P(AO B

A: Introduction: The union of any two or more sets yields a fully new set that comprises a mixture of…

Q: Let U be a universal set, and suppose A and B are subsets of U. (a) How are (x ∈A →x ∈B) and (x…

A: let U be a universal set and suppose A and B are subsets of U. (a) x∈A→x∈B and x∈Bc→x∈Ac are they…

Q: Let A, B be any sets with BCA. Then |P(B×B)[s|P(A×B)| O IP(AxB)|s|P(B×B)| O IP(AxB)|=|P(B×B)| O None…

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Q: Use an element argument to prove the statement that for all sets A, B, and C, if A ⊆ B then A ∪ B =…

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Q: Let A and B be sets. Then B (B – A) -

A: Complement of set A =1-A

Q: Let A and B be sets. Prove that (A − B) ∩ (B − A) = ∅.

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Q: Let A, B, and C be sets. Prove A × (B\C) = (A × B)\(A × C).

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Q: If A, B, C are sets, then a. A\(BUC) = (A\ B)(A\C) b. A\(BnC) = (A\ B)U(A\C)

A: We know that for two sets A and B: A \ B = A∩Bchere Bc is the compliment of set B Distributive Laws:…