When A, B, and C are sets, A∩(B⋃C) = (A∩B)⋃C if and only if     A ∩ C ⊆ A ∩ B     C ⊆ A     A ∩ B ⊆ A ∩ C     A ∩ B ∩ C = ∅     C ⊆ B Choose correct answer.

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

A:

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

A:

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

A:

Q: Prove that if A1,A2,…,An and B are sets, then (A1−B)∪(A2−B)∪⋯∪(An−B)=(A1∪ A2 ∪⋯∪ An)−B.

A: To Prove- Prove that if A1, A2, ...., An and B are sets, then A1 - B ∪ A2 - B ∪ .... ∪ An - B = A1 ∪…

Q: If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

A: P × Q = {a,b,c} × {r} = {(a,r) , (b,r) , (c,r) } Q × P= {r} × {a,b,c} = { (r,a) , (r,b) , (r,c) }

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: For every two sets A and B, if A–B = B – A , then A-B=Ø. For every two sets A and B, ANBCA-B.

A: (4) Given A and B are two set such that A-B=B-A for every A and B We have to show that A-B=∅ Now,…

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

A:

Q: Prove formally that A\ B= A\(An B), for any sets A and B.

A:

Q: If sup A < inf B for sets A and B, then there exists a c€R satisfying a <c<b for all a EA and bEB.

A:

Q: Let A, B be any sets with ACB. Then O None of these O IP(BxB)|s|P(A×B)| O IP(A×B)=|P(B×B) O…

A:

Q: Prove that if A1, A2, ..., A, are any n > 2 sets, then A NA2 N …… A„ = A¡ UA2 U.…UA..

A: We will  prove the given statement using mathematical induction method.

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. Use an element argument to prove that (A - B) - C≤A-C.

A:

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

A:

Q: Let A, B be any sets with ACB. Then * O None of these O IP(A×B)|<|P(B×B)| O IP(A×B)|=|P(B×B)| O…

A: Power Set: If A is any set, the collection of all its subsets is another set is called the power set…

Q: Suppose that A, B, and C are sets such that A ⊕ C = B ⊕ C. Must it be the case that A = 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: b) BC A' iff A o B = ¢

A: Solution is given below:

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

A:

Q: For all sets A, B, and C, if A C B and BnC = 0 then An C = 0. Construct a proof for the statement by…

A:

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

A:

Q: Let A and B be sets. Prove that if A = B, then A+ = B+.

A: Given: A and B To find: Solution

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

A:

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

A:

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: 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: 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: If A and B are sets containing finitely many elements, then |A x B| =|B x A|.

A:

Q: Let A,B be sets. Prove that AAB = if and only if A= B

A:

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

A: Let us consider four non empty sets A, B, C and D such that A x B=C x D if and only if A=C and  B=D…

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

A: We have to give a counter example for  A – C = B – C imply A = B.

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 A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and S, the…

A: The set A=t,u,v,wS1 be the set of all subsets of A that do not contain wS2 be the set of all subsets…

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

A: Given a statement

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

A:

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: Let A=​{peach, kiwi, tomato, raisin​}, B=​{lemon, watermelon​}, and C {tomato, lemon, pear,…

A: Let A and B be two sets .         1.)  n( A∪B)=nA+n(B)-n(A∩B)         2.) n(A∪B)= n(A-B)+n(A∩B)+ n…

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

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”.