(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 U C = B UC = A = B. (c) [AnC = B n C] v [A U C = B UC] =A = B.

Q: Prove for all sets of A, B, that P(A) U P(B) is a subset of P(AUB).

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: D. Let A, B, and C be subsets of some universal set U (a) If ANBC C and A° N B C C, prove that B CC

A:

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: The set S = {x | x is a continent}. A. S = {N. America, S. America, Europe, Asia, Africa, Australia,…

A: Given:  ( The set S = {x | x is a continent}  Then write the set S

Q: Prove the following statement using element proof: 1. For any four sets A, B, C, and D, if C ⊆ (D ∪…

A:

Q: Does there exist a non-empty open set A and two elements in A that are farthest apart (among all…

A: There are no two elements that are farthest apart in a non-empty open set. Justification : Let 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: Show that for all sets A, B and C, If A CB, then B CA.

A:

Q: Is the following biconditional statement true or false? Justify your conclusion. If it is found to…

A:

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: Given a universal set U for a set X , if AC X , then (U – X) n A = Ø

A: Given a universal set U for a set X and A⊆X We shall prove it by contradiction method. Let us assume…

Q: Prove or Disprove: The set A = {e^x : x × R} is uncountable, where R is the set of real numbers.

A:

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

A: Prove that : (A ∩ B)' = A' U B'

Q: ℘(A) ∪ ℘(B) ⊆ ℘(A ∪ B). Is ℘(A) ∪ ℘(B) = ℘(A ∪ B)? Either provide a proof to show that this is true…

A:

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

A:

Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: The solution is as shown below

Q: Đ A is a closed set.

A:

Q: Let C and D be subsets of a universal set U, then (C ∪ D) ⊆ (C ∩ D).

A: Given C and D are two subsets of universal set U.

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: Consider the following statement. For all sets A and B, A° U B° C (A U B)°. The following is a…

A:

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

A: let B and C be the subsets of some universet x1 then prove that (c-B)' = BUC'

Q: 4.2. Let S be the open set consisting of all points z such that |2| < 1 or |z – 2| < 1. Show that S…

A: Connected set: If any two points of a given set can be joined by a continuous polygon arc such that…

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

A:

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

A:

Q: 4. Let A and B be sets. (a) If A and B are subsets of the same universal set U (so A × B is a subset…

A: The definition of complement is given at the end of proof

Q: Disprove the following statement by finding a counterexample. For all sets A, B, and 6, C, An (BUC)…

A:

Q: Let A and B be subsets of a universal set U, Prove that ACB if and only if B C A.

A: By definition, B′⊂A′ implies exactly two things: Every element of B’ is in A’ There exists an…

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: ) Let A and B be subsets of a universal set U, show that (An B)U (A n B) = A AC B if and only if B C…

A:

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

A: The solution are next step is

Q: b) BC A' iff A o B = ¢

A: Solution is given below:

Q: Prove that if A is a set then so is {A}!

A:

Q: Which of the following is true for any set A?

A: HERE FOR TRUE SENTENCE FOR ANY SET A . EMPTY SET IS  SUBSET OF ANY SET

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

A:

Q: Consider the following theorem of set theory: For any two sets A, B, [A U (B – A)] = A U B. a.…

A:

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: Show that for any sets A and B,A = ( A ∩ B ) ∪ ( A – B ) and                    A ∪ ( B – A ) = ( A…

A: Let A and  B be any two sets and U be the universal set.

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: Let R and S be two posets on a set X. Are RNS, RUS, R\ S, also posets on X as well? If they are,…

A: Given R and S are two Poset on a set X. (1) Consider R∩S. Since R and S are poset, therefore each…

Q: Consider the following statement. For all sets A and B, AC U BC C (AU B)C. The following is a…

A: The solution are next step

Q: Prove that if A, B.C are subsets of a universal set U, then AU(BnC) C (AUB)n(AUC)

A: use the basic property of subset and set theory.

Q: Prove that a set A is connected iff A is and interval.

A:

Q: Let A, B, C be arbitrary finite sets from the same universal set U. - (a) Is it true that A - B C (A…

A: SOLUTION-

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

A:

Q: - A non-empty set E in R is connected if and only if it is an interval

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”.