Let A = {a, b, c},B = {b, c, d},and C = {b, c, e}.(a) Find A ∪ (B ∩ C),(A ∪ B) ∩ C,and (A ∪ B) ∩ (A ∪ C).(Enter your answer in set-roster notation.) A ∪ (B ∩ C) (A ∪ B) ∩ C (A ∪ B) ∩ (A ∪ C) Which of these sets are equal? A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) A ∪ (B ∩ C) = (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C) (A ∪ B) ∩ C = (A ∪ B) ∩ (A ∪ C) A ∪ (B ∩ C) = (A ∪ B) ∩ C(b) Find A ∩ (B ∪ C),(A ∩ B) ∪ C,and (A ∩ B) ∪ (A ∩ C).(Enter your answer in set-roster notation.) A ∩ (B ∪ C) (A ∩ B) ∪ C (A ∩ B) ∪ (A ∩ C) Which of these sets are equal? (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) A ∩ (B ∪ C) = (A ∩ B) ∪ C A ∩ (B ∪ C) = (A ∩ B) ∪ C = (A ∩ B) ∪ (A ∩ C) c) Find (A − B) − Cand A − (B − C).(Enter your answer in set-roster notation.) (A − B) − C A − (B − C) Are these sets equal? Yes No

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set. A ∪ B

A:

Q: For the sets A, B, and C (let A = {1, 2, 3, 4}, B = {1, 3, 5) and C = {2, 4, 5}), find: A x B, (An…

A: 1,  A × B: The Cartesian product of A and B represents all ordered pairs where the first element…

Q: Let 4, B, and C be sets. Show that a) (A - B) – CSA C. b) (A - C) n (C- B) = 0.

A: Answer

Q: State whether the following claim is true and explain why. (a) Claim: For all sets A, B, and C: (A –…

A:

Q: Define the sets A, B, C, and D as shown. Find A ∪ (B ∩ D

A: We have to define A, B, C and D first and then find the A∪B∩D. Assume  A=1,2,3,4,5,6,7 B=1,2,6,7,8,9…

Q: Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that(i) A × (B ∩ C) = (A ×…

A: i) Answer(i) A × (B ∩ C) = (A × B) ∩ (A × C) (proved)

Q: Given two sets A and B, are the sets A − B and B − A necessarily disjoint? Give a proof or a…

A: Given: A and B are two sets. We have to explain A-B and B-A is necessarily disjoint.

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: Is it true that for any sets A and B,        P ( A ) ∪ P ( B ) = P ( A ∪ B )? Justify your answer.

A:

Q: Example: If A = {1, 2, 3,4,5}, B = {1, 2,4}, C = {2, 3,5}, verify that, A×(B∩C) = (A×B)∩(A×C)

A: Simplify LHS: LHS=A×B∩C=1, 2, 3, 4, 5×1, 2, 4∩2, 3, 5=1, 2, 3, 4, 5×2=1, 2, 2, 2, 3, 2, 4, 2, 5, 2

Q: Consider the sets: A={a,b,c} B={b,c,d} C={a,c} D={d,c,b} For each statement below, state whether the…

A:

Q: Does A − (B − C) = (A − B) ∪ C hold for all sets A, B, and C? Prove or give a counterexample for…

A:

Q: Let A and B be two sets. We denote A- B = { x | x∊A and xÏB}. Prove that A∪B=(A−B)∪(A∩B)∪(B−A).

A:

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: Given 2 sets A and B with A=blue, red, green, orange, yellow, purple  and  B=pink, black, orange,…

A: The given sets are A=blue, red, green, orange, yellow, purple and B=pink, black, orange, yellow,…

Q: A  =  {E2, E4} B  =  {E1, E3} C  =  {E1, E4, E5} P*A=0.4 P*B=0.4 P*C=0.6 P(A U B)=0.8 Find  AC.…

A: Solution-: Given:  A={E2,E4} B={E1,E3} C={E1,E4,E5} We want to find  (a) Ac=? (b) Cc=? (c) A∪Bc=?

Q: Let A = {July, John, James, Jared, Jeniffer, Jelly}, B = {John, Jelly, Jared}, and C = {Irina,…

A:

Q: Let A, B, C be sets. Prove that if C ⊆A, then A −(B −C) = (A −B) ∪C. Analogously, for any real…

A:

Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

A:

Q: Find the union of the sets. {e, m, p, t, y}∪∅

A: we have to find the union of the sets. e,m,p,t,y∪∅

Q: Let A, B, C, and D be sets. Prove that (a) if CCA and DCB, then COD CANB.

A:

Q: let A, B ⊂ R, and suppose A and B are closed. Prove that A ∩B is closed. Hint: You might try showing…

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: Which of these sets are equal? O An (B U C) = (A n B) U (A n C) An (B U C) = (A n B) U c O An (B U…

A:

Q: If A ⊂ B, can A and B be independent under any circumstances? Explain

A:

Q: Let A = {June, John, James, Justin, Jeffrey, Jelly}, B = {John, Jelly, Justin}, and C = {Irina,…

A: Let A = {June, John, James, Justin, Jeffrey, Jelly}  B = {John, Jelly, Justin} C = {Irina, Irena,…

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…

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”.