(3) For sets A, B, and C in some universal set U, prove or disprove the following. (a) AnC = B nC =A = B. (b) A UC = B UC = A = B. (c) [An C = B n C] v [A U C = B U C] =A = B. (d) [An C = B n C] ^ [A U C = BUC] =A = B. V

Q: Disprove the following statement. For all sets A, B, and C of some universe U, (AAB)U (ANBNC) =…

A:

Q: Suppose that E1 and E2 are measurable sets. Prove that m(E1 U E2) + m(E n E2) = m(E1) + m(E2).

A: We have to prove that the given statement.

Q: Let A and B be subsets of a universal set U and suppose n(U) = 300, n(A) = 150, n(B) = 120, and n(A…

A: Please see the below explanation.

Q: Let A and B be subsets of a set X. Prove that if A ⊆ Bc, then A and B are disjoint.

A:

Q: [3.12] Let S be a nonempty convex set in R", and let f. R" → R be defined as follows:

A: Let S be a nonempty convex set in Rn, and  Let f:Rn→R be defined as follows:…

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

A:

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

A: First show if A∪B=A∩B then A=B, then show that if A=B then we have A∪B=A∩B.

Q: Let S and T be sets. Prove that SUT = T iff S is a subset of T.

A: To Prove S∪T=T iff S is a subset of T

Q: (2) Show that if f has support in a compact set A CR and g has support in a compact set B C R then f…

A:

Q: 3. Let {B;}je1 and {C;};e1 each be a family of mutually disjoint sets. If B; = C; for each i e I,…

A: Answer :

Q: Let A and B be sets and suppose that A U B = B. Prove that ACB.

A:

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: prove for every two sets A and B that A=(A-B)U(A n B)

A: To prove: We want to prove  for every two sets A and B that A=A-B∪A∩B

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

A:

Q: If A and B are nonempty, bounded, and satisfy A c B then sup A < sup B. If sup A < inf B for sets A…

A: a) Given that A,B are non empty sets, and A⊂B The objective is to show that supA≤sup B Since it is…

Q: Theorem 1.2.2 (De Morgan formulae) For any two sets A and B, (i) (A U B)' = A'N B' (ii) (AN B)' = A'…

A:

Q: (A'n B) = A' U B'.

A: Prove that : (A ∩ B)' = A' U B'

Q: Let B and C be the subsets of some universal set X then prove that (C N B')' = BU C'

A:

Q: Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C) U(B – C) by using laws of…

A: I have just used the law of sets

Q: Theorem 5.25. Let A, B, and C be sets. Then 1. A× (B N C) = (A × B) N (A × C) 2. A × (B U C) = (A ×…

A:

Q: 3. (a) Prove that A\(BnC) = (A\B)U (A\C) for any sets A, B, C

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Prove that for any sets A, B, C, ANB = AN C and AUB= AUC if and only if B = C. %3D Prove that for…

A:

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B)n (AUC)

A: To prove:- Prove that for any sets A, B, C we have AU (B∩C) = (AUB)  ∩(AUC) Method :- I use venn…

Q: Prove that for all sets A and B, A – B = AN B

A:

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: 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: 1. Let A, B, and C be subsets of some universal set U. Prove the following statements from Theorem…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: Show every possible 1-1 correspondence between the following sets. {A,B} and {a,b}

A: The solution are next step is

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: Prove that P(Sn T) P(S) n P(T) for any sets S and T

A: Let, S and T be a any set. also, P(S) be any power set of S and P(T) be any power set of T.x∈P(S∩T)…

Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: Prove that if R, S, and T are nonempty sets, then R×T ⊆ S×T if and only if R ⊆ S.

A:

Q: Let A and B be sets. Let X = A n B, Y = A \ X and Z = B\ X. Prove that X n Y = Ø, X n Z = Ø, Y n Z =…

A:

Q: Prove that for all sets A, B, and C, if CCB-A, then AnC=0.

A:

Q: If A is a countable set and B is an uncountable set, then the MOST we could ever say about A U Bis…

A: We have given the three MCQ questions about countability and uncountability . We have to choose the…

Q: Prove that, for any sets A and B, it is true that A ⊆ B iff A ∩ B = A.

A: Use the following definitions, to obtain the solution. Let A and B be any two sets. The…

Q: . Let S and T be sets. Prove that S n (S U T) = S and S U (S n T) = S.

A: Since you have posted multiple questions, we answered the first question for you. If you want any…

Q: Prove or disprove that for all sets A, B, and C, we have a) A × (B ∪ C) = (A × B) ∪ (A × C). b) A ×…

A:

Q: 2. Disprove the following statement. For all sets A, B, and C of some universe U, (AAB)U (An Bnc) =…

A: Given: A, B and C are sets in some universe U. To disprove: A∆B¯∪A¯∩B∩C=A∩B∪C \ A

Q: (iv) Prove that for any sets A, B,C we have A U (B nc) = (AU B) n (AUC)

A:

Q: One of the following statements is True a) Z is connected set if there exist two non-empty separated…

A: This question is related to Topology .

Q: Prove the following: For all sets A and B, if A C Bº then AN B = Ø.

A: Assume that for some A⊂Bc then A∩B≠∅. Thus, there exits x∈A∩B.

Q: T have to show rigorous proof of the inclus (An B) x C c (Ax C)UCBXC) 1,B.and C, Sets non-em pty of…

A:

Q: For every set A, {Ø} C A.

A: We use the definition of an empty set and subset of a set to answer the given question.

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: Let A and B be two finite sets such that |A| = 20, |B| = 28 and |A U BI

A: Given A=20B=28A∪B=36

Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A…

A: A set is a collection of elements. The elements that make up a set can be any kind of mathematical…

Q: Prove that for all sets A and B and nEZ, n ≥ 1, the following holds: 72 11 (a) U(A\B) = (UA) \ B;…

A:

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

A:

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.