Suppose A,B and C are sets with C∕= ∅. Prove that if A×C= B×C, then A= B. Why is it necessary that we specify that C∕= ∅?

Q: If A and B are any two sets, then A ∩ (A ∪ B) is equal to a. A b. B' c. A' d. B​

A: It is given that A and B are any two sets. It is required to obtain the value of A∩A∪B.

Q: . If A and B are sets in a universal set U, then AUB=AnB.

A: We proved this by wave diagram

Q: Prove the following statements if they are true and give a counter-example if they are false. a) For…

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Q: Determine which of the following sets are equivalent. ĀU (BNC) BUC) 2) A U B 3) An (BUC) Only 1) and…

A: Answer belowExplanation:To determine which of the given sets are equivalent, let's first simplify…

Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: Please refer to the solution in next step.

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: O ACBiff P(A) C P(B). O ACBIF and only if AU B= B (A x B) U (C x D) (AUC) x (BU D)

A:

Q: Prove that {9":ne Q} = {3":neQ}.

A: Two sets A and B are equal i.e. A=B if and only if

Q: 5. Consider the sets A = 0 and B = {0} and C= {1,0}. Find each of the following sets, if it is…

A: The given sets are                       A=ϕ and B=ϕ and C=1,ϕ. Here the set A is the empty set,…

Q: Suppose that A = all current students at MPC and B = all current students at Hartnell (and U = all…

A: Given, A = all current students at MPC and B = all current students at Hartnell

Q: . If A and B are sets in a universal set U, then AUB=AnB. A-(BnC)=(A-B)U(A-C). . If A, B and C are…

A:

Q: 3. Let A and B be two sets. Use set operation properties to prove the identity ,AÐB = AUBU (AO B).

A: To prove the identity

Q: Let A = {June, John, Jill, Jared, Jeffrey, Jelly}, B = {John, Jelly, Jared}, and C = {Irina, Irena,…

A: We have given that set  Let A = {June, John, Jill, Jared, Jeffrey, Jelly}, B = {John, Jelly, Jared},…

Q: 3. AnBCC. Prove the following statement: For all sets A, B, and C, if BCC, then

A:

Q: 1. Determine which of the following statements are true for all sets A, B, C, and D. If a double…

A: .

Q: 4. Suppose that A and B are sets such that AnB = Ø and A UB= U. Use a Venn diagram to show what A n…

A: Ac∩Bc=ϕExplanation:[Note: A Venn diagram can be represented by any closed figure, whether it be a…

Q: 1. Let A, B, and C be sets. Given A C B, show that (a) AnC C BnC. (b) ВС А.

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Q: 15. If A, B and C are sets, then (AnB)-C=(A-C)n(B-C). m

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Q: Is this true or false and why : ∅ ⊆ {1}

A: Given: It is given that ϕ⊆1. To find: We have to determine whether the given statement is true or…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

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Q: 10 b)  Let A, B, C and D be sets. Prove that C ⊆ A and D ⊆ B, then C ∪ D ⊆ A ∪ B

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Q: Sets B and C are subsets of the universal set U. These sets are defined as follows. U={f,k,m, x,y }…

A: It is given that: U=f,k,m,x,y,B=k,y,C=f,k,m Therefore the complementary sets of B and C are:…

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a, b) : a € A…

A: The answer for the above question is given below please do upvote if you like the solution thank you

Q: O (A x B) U (C x D) C (AUC) x (BUD)

A: Please check step 2 for the solution.!

Q: Draw figures showing two sets A and B, so that B C A. DO NOT draw the set elements.

A: As we know the meaning of B ⊆ A is that B has few or all elements equal to the set A B ⊆ A subset…

Q: But change the problem to say A={1,5,7,11}, B={3,5,7}, C={3,7,9,11}

A: The union of two sets contains all the elements contained in either set (or both sets).The union is…

Q: What is (A∪B)c where A={5,11,3,8,9} , B={99,5,11,2,4} and Universal Set…

A:

Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set A × B = {(a, b) : a E…

A:

Q: (BOC)=(A-B)u(A-C). 11. If A and B are sets in a universal set U, then AUB=AnB. 12. If A, B and C are…

A: To prove the equality A - (B ∩ C) = (A - B) ∪ (A - C), we need to show that each set is a subset of…

Q: 17. If A,B and C are sets, then Ax (BnC) = (A x B) n(A x C).

A:

Q: 18. If A,B and C are sets, then Ax (B-C)= (A x B)-(AXC).

A: By the using of definition we prove this.

Q: 5. Let A, B, and C be sets. Prove or disprove that if AUB ANC, then A & C or BJA.

A: We disprove the statment with suitable example

Q: 1. What kind of set is V = {x ∈ N I x < 1} ?

A: Given,  V = {x ∈ N I x &lt; 1}

Q: 3. Let U = {1,2,3,4,5}, B = {4,5} and A and B are non-empty sets. Contruct the venn diagram and find…

A: Venn diagram is the pictorial representation of the finite number of groups. It used to understand…

Q: I. Let the universal set U {1,2, 3, ..., 10} . Let A = {1,4, 7, 10}, B= {1,2, 3, 4, 5}, and C = {2,…

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Q: Let U= { 1,2,3,...,20}. Let A, B, C be the subsets of U. Let A be the set of all numbers, which are…

A:

Q: 14. If A,B and C are sets, then (AUB)-C=(A-C)u(B-C).

A: To prove the equality (A∪B)-C = (A-C)∪(B-C), we need to show that any element x belongs to the…