Let A, B, and C be sets. Use the the identity A − B = A ∩ B, which holds for any sets A and B to show that (A − B) ∩ (B − C) ∩ (A − C) = ∅

Q: If A and B are finite sets, then A ∪ B is also a finite set

A: Let A and B are finite sets. We need to show that , A ∪ B is also finite set. case 1) If A = B = ϕ A…

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

A:

Q: Let A, B and C be sets. Use an element argument to prove the following. (A - B) n (B-A) = 0.

A:

Q: Prove that for sets A and B, if A C B then P(A) C P(B

A:

Q: Prove that if A and B are transitive sets, then A ∪ B and A ∩ B are transitive sets

A:

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

A:

Q: Let A, B, and C be sets. Using Venn Diagram and Set identities, show that a) (A∪B)⊆ (A∪B ∪C). b)…

A: Follow the steps.

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

A:

Q: Suppose that A and B are finite sets. Prove that A U B is finite, and |A U B| = |A| +|B| -|A n B|.…

A:

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: Prove that for sets  A and B,  we have  (A∪B)−(A∩B)=A−B if and only if B⊂A.

A: By theorem we know that,            A⊂B if and only if A∩B =A and  A∪B =B

Q: If A and B are two sets such that A ⊂ B, then what is A ∪ B ?

A: Let us understand it by and example,   Let, A={1,2,3} and B={1,2,3,4,5} Here we can see that A ⊂ B

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

A:

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

A: True.

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

A: Let us consider four set A , B, C and D then AxC=BxD if all the elements of A are same as all the…

Q: For an element to be in the intersection of sets A and B, the element must be in set Am in set B.…

A: Any elements of A intersection B must be in set A and in set B

Q: If A C BỊ U B2 where B1 and B2 are disjoint open sets and A is compact, show that An B1 is compact.…

A: To Show- If A ⊆ B1 ∪ B2 where B1 and B2 are disjoint open sets and A is compact, show that A ∩ B1 is…

Q: Suppose that each of A, B, and C is a set and each of BnC, A–(BnC), A-B, A-C, and (A – B) n (A – C)…

A:

Q: Let A, B, and C be sets. Does A- B= A –C imply B = C? If so, prove it. If not, give a…

A: Let A, B and C are sets. We have to find out that A-B = A- C implies B = C or not If not then we…

Q: Suppose A and B are sets. Prove that A – B = AN B.

A:

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: Prove that if A and B are sets, then (A∩B)∪(A∩B^' )=A

A: To prove : A∩B∪A∩B'=A   Let x∈A∩B∪A∩B' ⇒x∈A∩B or x∈A∩B' ⇒x∈A and x∈Bor x∈A and x∈B' In either of the…

Q: |(A ∪ B)\(C ∪ D)|

A: We have to give a formula for |(A ∪ B)\(C ∪ D)| in terms of the sizes of the four sets A, B, C, D…

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: Let A, B1, B2 and C be sets and let B AC BỊ and C C B2. Bị × B2. Consider the statement, "If A x C C…

A:

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

A:

Q: Prove that if A and B are sets, then A - B = An BC.

A:

Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

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

A:

Q: For any sets A, B, C  use element argument to prove that  (A-B) - C is a subset of A - C

A: By the element argument we prove the given problem as follows :

Q: Show that if A and B are sets, then P(A) u P(B) C P(A u B), where P(A) denotes the power set of A

A: For a set A, the set of all its subsets is called the power set of A. Now, consider two sets A and…

Q: Show that if A and B are sets, then P(A) u P(B) c P(A u B), where P(A) denotes the power set of A

A:

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 O B=c O…

A: A, B, and C are non empty sets

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 sets. Prove that AAB = if and only if A= B

A:

Q: Let A, B, and C are three sets, prove that B×(AnC)=(B× A)^(B×C)

A: Given 3 sets A, B and C. We have to prove that B×A∩C=B×A∩B×C. For this, we have to show that…

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: Show that if A and B are finite sets, then A ∪ B is a finite set.

A:

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: For an element to be in the union of sets A and B, the element must be in set A in set B. but not…

A:

Q: Let A, B, and C be sets. Prove that if A CB and B C C, then A C C.

A: Let, x belongs to A. Since, A is a subset of B, so, x belongs to A implies that, x belongs to B. So,…

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

A:

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

A:

Q: Let A and B be sets. Define precisely (but concisely) what it means for A to be a subset of B

A: Let, A and B be setswhat it means for A to be a subset of B.

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

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.