Let A and B be any given sets. Use set builder notation and logical equivalences to show that AUB=An B.

Q: Identify the set expression modeled by the attached Venn Diagram. Simplify the expression using…

A: According to Demorgan’s rule,

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

A:

Q: Provide 2 examples of sets with |A| = 4, |B| = 3, |AUB| = 6

A: Number of elements in set A is 4, in set B is 3 and in set A U B is 6.

Q: Let X={a,b,c} and Y=∅. What is X∩Y? If the set is empty type ∅, otherwise write your answer in…

A:

Q: Fill in the blank so that the resulting statement is true. The symbol E is used to indicate that an…

A: Given: The statement is "The symbol ∈ is used to indicate that an object _______ of a set. To fill:…

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: The set subtraction law states that A – B = ANB. Use the set subtraction law as well as the other…

A: The given statement: For any sets A and B, A∩B-A=∅.

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: Perform the given set operation. X ∩ ∅ for any set X

A: The given set is, X ∩ ∅ The objective is to perform the set operation.

Q: If R1 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is also an equivalence…

A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

Q: Determine if the union/intersection of two open sets is always open then determine if the…

A:

Q: Prove or disprove: For all sets A,B and C: (A-B)-C = A-(BUC).

A:

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

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

A:

Q: How do i approach the following question?  Let A and B be sets. Prove that A ∪ B = A ∩ B if and…

A:

Q: Let A = {a,b,c,d,e}, B = {a,b,c,d,e,f,g,h}, and U represents a Universal Set of…

A:

Q: Consider two sets A and B such that A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. Find the set C…

A:

Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

A:

Q: Use the set definitions A = {a, b} and B = {b, c} to express the elements in the powerset P(A) ∩…

A:

Q: Write the following sets in set-builder notation. Answer must restate set membership in some way.…

A: The given sets are     A= { 2,4,8,16,32,...}  and B={1,5,9}

Q: Let ai = [250] -10 and a2 = h [4] The set {a1, a2} will span R² unless h = (If there are no values…

A: