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

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

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Q: - For all sets A, B and C. Is (An B) U C =An (Bu C)? Justify your statement. You may ju

A: Yes, the above statement is false and the proof of above statement is given below:

Q: For all sets A B and c, of CAXC)- CBrC)# Ø, then A-B#¢.

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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: What can you say about the sets A and B if A ⊕ B = A?

A: The symmetric relation is described as, A ⊕ B =(A-B) U (B-A)

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: 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: What is the intersection of sets A and B?

A: The intersection of sets is a set which include the common of the two sets A and B. It is…

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

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Q: For any sets A, B, show that (A \ B)c = Ac ∪ B.

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Q: Is it true that for any sets A and B,        P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

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Q: Let A, B, and C are three sets, prove that C × (AN B)' = (C X A') U (C × B') CS

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Q: If A and B are sets; A and B denote the complements of the sets A and B, then set (A- B)U(B –…

A: Using venn diagram we solve this question.

Q: Consider the sets: A={a,b,c} B={b,c,d} C={a,c} D={d,c,b} For each statement below, state whether the…

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Q: For any sets A, B, and C; the distributive law states AU (B n C); that is a. (A U B) n (A U C) c. (A…

A: DeMogran's distributive law

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

A: The Venn diagram for 2 sets can be drawn as follows.

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

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Q: If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10…

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

A: A, B, C are any set, we need to show that (A-B) - C = (A-B) - (A-C) this can be done using the…

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

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

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Q: Show that if A and B are sets with A ⊆ B, then a) A ∪ B = B. b) A ∩ B = A.

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Q: Find the intersection of the sets. {r, e, a, l}∩{l, e, a, r}

A: Given:A=r,e,a,lB= l,e,a,rIntersection set:The set containing all elements of A that also belong to…

Q: Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example.

A: No, it is not true. EXAMPLE- Let A= {2}  B= {{2},3,4} C={{2},3,4,5,6} We can see here that,

Q: What is the union of sets A and B?

A: Assume the independent sets A and B. Set A = 0,1,2Set B = 4,5,6

Q: Let A, B and C be non-empty sets and let X= (A-B)-C and Y=(A-C)-(B-C) .Check whether X=Y or not.

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

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Q: Let A, B, C, D be sets. If A\ B CC\D, then ANDC B.

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Q: Consider sets A={1,3,5} and B = {2,4,6}. Find A U B

A: The given sets are A={1,3,5} and B = {2,4,6}. The union of any two sets is the set of all the…

Q: For any sets A  B, C, ( A ∩ B) ∪ C ≠ A ∩ ( B

A: Given that the sets A, B, C. Consider, A∩B∪C=A∪C∩B∪C.............(1) Consider,…

Q: Let A, B and D be sets. If A n B = Ø then prove that (A – B) – (B n D) = A.

A: Take x in left hand side and prove it belong to A and vice versa.

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

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Q: Are there sets A and B such that |A|=|B|,|A|=|B|, |A∪B|=10,|A∪B|=10, and |A∩B|=5?|A∩B|=5? Explain.

A: Given:A|=|B|, |A∪B|=10, and |A∩B|=5The Venn diagram is

Q: For any sets A and B, show thatP ( A ∩ B ) = P ( A ) ∩ P ( B ).

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Q: For any two sets A and B, if A=B,then A=B صواب ihi

A: Given a statement

Q: Consider the two sets A={a, e, i, o, u} and B={c, m, n, r, s, v, w, x, z}. Which of the following is…

A: Given :               The sets A = a,e,i,o,u   and B = c,m,n,r,s,v,w,x,z

Q: Prove that if A ~ B then P(A) ~ P(B).

A: Consider the provided question,

Q: Let A, B, and C be sets. Show that a) (A ∪ B) ⊆ (A ∪ B ∪ C). b) (A ∩ B ∩ C) ⊆ (A ∩ B). c) (A − B) −…

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Q: Let A, B, C be sets. Simplify (A∪(B∩C))∪((Bc ∩Cc)∪C)c

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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 finite sets with |A|=10, |B|=5, |A∪B|=12 what is |A∩B|?

A: Given,  |A|=10 |B|=5 |A∪B|=12 |A∩B|=?

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).

A: