Consider the following theorem. Theorem: For all sets A and B, if A C B, then A U B CB. Supply explanations for the steps in the proof of the theorem. Proof: Statement Explanation Suppose A, B, and C are any sets such that AC B. starting point We must show that A UBC B. conclusion to be shown Let x be any element in AU B. start of an element proof Then x is in A or x is in B. ---Select--- In case x is in A, then x is in B ---Select--- In case x is in B, then x is in B. tautology (p → P). So in either case, x is in B. proof by division into cases Thus every element in A UB is in B. since x could be any element of A U B Therefore, A UBCB --Select--- [as was to be shown].

Q: fer to the Venn diagram below. How many elements are in the set AUB? U A C n(AUB) = 22 12 36 50 3 B…

A: Solution

Q: Let A = {x € N|x < 7}, B = {x € Z] -4 < x-2<4}. And C = {x E R|x² + x - 12 = 0}. a) List the…

A:

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: nsider the following statement. For all sets A and B, AC U BC C (A U B)C. e following is a proposed…

A:

Q: I Let A = {1,3,5,7}, B = {1,2,3}, C = (6,7} and suppose the Universal set is U = {1,2,3, ..,7}. List…

A:

Q: Let S be a set. For every subset A of S we denote by A the complement of A in S. Show that for all…

A:

Q: O ACBiff P(A) C P(B). O ACBIF and only if AU B= B (A x B) U (C x D) (AUC) x (BU D)

A:

Q: For any sets A, B, and C, A \ (BUC) = (A\ B) U (A\ C). For any sets A, B,C, if AN B C C, then (A \…

A:

Q: Question 34 Determine whether the ff. proof is valid: for all sets A, B, and C, if AC B and BC C…

A:

Q: 2. Suppose A, B, and C are sets. Prove that (AUB) \C CAU (B \ C).

A: Introduction: We know that the difference property of two sets A and B as A/B=A∩B'.

Q: Proposition 1.43. A is the intersection of all closed subsets of X which con- tains A. Proof.…

A:

Q: Prove the following statement. Assume that all sets are subsets of a universal set U For all sets A…

A:

Q: Determine if the statement below is true or false. If it's true, give a proof. If it's not, give an…

A: Given that For all sets A,B,C we have  A∪B∩C=A∪B∩A∪C

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: Give an example of each of the following or prove that such a request is impossible. infinite family…

A: Here we have to give an example or prove that such a request is impossible. e) infinite family of…

Q: Which of the following is true for all sets S and T? Select one: O A. SOT SOT B. SOT SUT C. SUT SOT…

A: see below the answer and explanation

Q: Theorem: let S₁, S₂ be the collection of sets D (US) U (US). = US. SES, VS₂

A: Solution: Let S1  and S2  be  the  collection of sets.We  have  to show  that  ∪S∈S1S∪∪ sS∈S2=∪…

Q: Consider the following statement. For all sets A and B, (A U B) = A°U B. Which sentence below…

A: ANSWER :

Q: O (A x B) U (C x D) C (AUC) x (BUD)

A: Please check step 2 for the solution.!

Q: (4) Prove by contradiction, for any sets A and B, if ACA- B, then An B= Ø

A:

Q: An algebraic proof for the statement is given below. and Select the properties used Suppose A and B…

A:

Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: Using equality of sets, prove that (?∩?)′ = ?′ ∪?′

A:

Q: Given the sets Determine which one is a subset of the other. Prove that subset property by universal…

A: To determine which set is a subset of the other, we can try to find a counter-example where an…

Q: 7. A, B, and C are subsets of a set S. Prove the following set identities using the basic set…

A:

Q: Let A and B be sets prove the following. AC B if and only if A UB = B.

A:

Q: One set to rule them all, one set to find them, one set to bring them all and in the darkness…

A: Question: Is there a "set of all sets"? That is, does there exist a set U such that for all sets S,…

Q: Suppose that A and B are sets such that AC B. Which of the following must be true? Select all that…

A: The question is asking us to determine which of the given statements must be true if set A is a…

Q: Let S and T be sets. Identify all of the following statements that are equivalent to the statement…

A: Let S and T be sets and T⊆S. Now, T⊆S , which means set T is a subset of set S. A collection of…

Q: Let A and B be sets such that B (1) If A is finite, then B is finite. (2) If A is infinite, then B…

A:

Q: A, B, and C are subsets of a set S. Prove the following set listed in this section. Give a reason…

A: Introduction: Basic identities of a set: 1. commutative: A∪B=B∪A 2. ASSOCIATIVE: (A∪B)∪C=A∪(B∪C) 3.…

Q: 1) Negate the statement: If a is odd then then a2 is odd. 2) Find a counterexample for each…

A:

Q: Sets M and A are defined as follows. M={c, h, k} A = {a, c, g} Answer each part below. Write your…

A: Here we have to find intersection and union of given sets M and A.

Q: A, B, and C are subsets of a set S. Prove the following set identities using the basic set…

A: The solution to the given question is explained below.