How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and only if A = B. show it step by step with explanation please

Q: Find the intersection of the sets. {s, e, t}∩{t, e, s}

A:

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

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: When A and B are sets, and x is an element of the universal set, the property “x ∉ A − B” is valid…

A:

Q: Use an algebraic proof to show that for all sets X ,Y and Z : (X – Y)n ZC = x – (Y u Z) Do not…

A:

Q: Complete the proof using only set identities and definitions. Suppose A, B, and C are any sets. Then…

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: Let A, B and C are be sets. Show that we can have AnB= AnC without B=C

A:

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

A:

Q: et A, B, C and D be sets. Prove that (AnB)u(CnD)=(AUC) n(BUC) n(AUD)n(BUD)

A: The set A∪B contains all the elements that are present either in set A or in set B. The set A∩B…

Q: True or False? 9. Let A, B, and C be any sets then C − (A ∩ B) = (C − A) ∪ (C − 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: Use element argument to prove the statement. Assume that all sets are subsets of a universal set U,…

A: The given statement is 'for all sets A, B, and C, A ∩ (B − C) = (A ∩ B) − (A ∩ C).'

Q: Set U is the set of farms in a certain country. Set A is the set of farms in the country that…

A: Given that , U = Set of farms in a certain country A = Set of farms in the country that produce corn…

Q: Let A, B and C be arbitrary sets. Does it always hold that A ∪ (B × C) = (A ∪ B) × (A ∪ C) ?

A: No, this is not true in general. For example, consider the following :

Q: True or False?

A:

Q: Determine if each statement is true or false. 1. If A not equal to B then A ∩ B = empty set. 2. If…

A: we will be using basic set theory to answer these questions

Q: Let A, B and C be sets. Consider the following statements. Which of them are true? 1. Ax B = B×A 2.…

A: Given that A, B and C are sets. Note: According to Bartleby guidelines we can solve only first three…

Q: (c) A \ B = A \ (An B). (d) A = (ANB) U (A \ B).

A:

Q: Prove for every two sets A and B that A∪B= (A-B)∪(B-A)∪(A∩B)

A:

Q: Let A, B and C be sets. Use the algebra of sets to verify each statement. Suppose, A AB -(A-B)u…

A:

Q: Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. Does…

A: The equality A∪B=A+B is not always true for every sets A and B. It is true only when A and B are…

Q: prove the following statement If A, B, and C are sets, then A - (BnC) = (A - B) U (A - C). Suppose…

A: Since you have posted a question with multiple sub ports, we will provide the solution only to the…

Q: (LP4) Here are two definitions about sets: Let A be a set. The set A is called the compliment of A…

A:

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: Prove the statement below.

A: Given, A and B be any sets. To prove that (A∩B)⊆(A∪B).

Q: True or False? 7. If A and B are two sets such that A ∪ B = A ∪ C then B = C.

A: Given: If A and B are two sets such that A ∪ B = A ∪ C then B = C.  We check that it is true or…

Q: denumerable. Apply the definition and prove that the set A = {₁, {} ... } is

A: An infinite set is denumerable if it is equivalent to the set of natural numbers I.e there is a…

Q: Find the intersection of the sets. {w, y, z}∩∅

A: Given, w,y,z∩∅we have to find intersection of the sets.

Q: Which of the statements below must be true for any sets A and B? Select all that apply. □ A. ANBCA…

A: The question is asking us to determine which of the given statements about sets A and B must always…

Q: Prove if the statement is true or false. For all sets A, B, and C: (A ∪ B) ∩ (A ∪ C) ⊆ Ā ∪ C…

A: I have given the answer in the next step. Hope you understand that

Q: The statement is either true or false. The statement is either true or false. If it is false,…

A: To Check: Whether the following statements are true or false: (a) Fora,b,c∈ℕ. at least a-b, a+c, and…