a and b be disjoint subsets of the universal set U. Assume n(U) = 110, n(A)=50 and n(B) = 25. Find n(Ac U B)

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: Let R be the equivalence relation on the set A ={ a, b, c, d } induced by the partition ( {a,b,c};…

A: Given A=a, b, c ,dpartitiona,b,c; d

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 about disjoint subsets A and B of a universal set U, except assume that n(U)=100, n(A)=30, and…

A: Given, n(U)=100 n(A)=30 n(B)=50 n(A′∪B)=?

Q: Let ‘E’ & ‘F’ are any two non-empty sets and there order are as follows;…

A: given let ‘E’ & ‘F’ are any two non-empty sets and there order are as follows;…

Q: Compute: (a)    n(A ∪ B) (b)    n(Ac) (c)    n(A ∩ Bc)

A: n(A ∪ B)= n(A)+n(B)-n(A ∩ B) n(Ac)= n(U) - n(A)  n(A ∩ B c)= n(A)-n(A ∩ B) Given that n(U)=200,…

Q: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {a, b, d, e}, B =…

A: Given Universal set is, U = {a, b, ..., i, j}. & A = {a, b, d, e}, B = {a, d, h, j}, and C = {a,…

Q: Find an example of nonempty, distinct sets A, B, C for which (ANB) UC = (AUB) nC.

A:

Q: Let A {a1, a2, ...} and B = {b1,b2, ...} be countably infinite sets. %3D Prove that A × B is a…

A:

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

A:

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

A: Prove that : (A ∩ B)' = A' U B'

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

A:

Q: Let A and B be subsets of a universal set U and suppose n (U) = 275, n(A) 100, п (В) = 70, п (An B)…

A: If A is subset of universal set U, then n( Ac ) =n(U)-n(A).

Q: Consider S to be the universal set. Let X = (AUB) nC and Y = (AnT)U (An B). %3D Write out the…

A:

Q: Prove that for any sets A, B, C, ANB = AN C and AUB= AUC if and only if B = C. %3D Prove that for…

A:

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

A:

Q: Use the element method for proving that a set equals the empty set to prove that for all sets A, B…

A:

Q: Find two infinite sets A and B so that A UB, AN B,А — В аnd B — А are all infinite sets. Show the…

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. 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: Let A and B be sets. Prove that the intersection of A and B is is a subset of the union between A…

A: To show that the elements which are common to both A and B belong to either A or B.

Q: Determine whether the following theorem is true or false: For all sets A, B and C, if A is a subset…

A: If X is a strict subset of Y, but X is not equal to Y which means there exists at least one element…

Q: Let U be the universal set with disjoint subsets A and​ B, where n(U) = 37​, n(A) = 8​, and n(B) =…

A: first we will find the value of n(A'∩B') we know according to De Morgan's law  A'∩B' =…

Q: Let A and B be any sets. Show that: (a) A – B, B - A, and An B are disjoint with each other. (b) A =…

A:

Q: Prove that for all the sets A,B,C if  B∩c  ⊆ A THEN (C-A)∩(B-A) = empty se

A: Given that: B∩C⊆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: Determine whether or not the following is true: for all sets A, B and C, (AUB) (C\A) = AU (B\C); If…

A:

Q: Give an example of sets {An}n≥1 such that for each n ≥ 1, the set An ⊂ [0, 1] is both compact and…

A: Construct sets Ann≥1 such that for each n≥1, the set An⊂0, 1 is both compact and connected, but the…

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

A: This is a valid proof.  Graphical presentation of the above statement is as follows.…

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

A:

Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 115, n(B) = 70, and n(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: Let the universal set be the set R , and let A={xER| 0≤ x <4 } B= {XER| 2<x≤10} Find  a. B-A  b.…

A: Given A= { x ∈R :0≤ x &lt;4 }, B= {X∈R : 2&lt;x≤10} Given universal set be the set R.

Q: Let A, B, and C be sets. Use the the identity A − B = A ∩ B, which holds for any sets A and B to…

A: Identity Used: A-B=A∩BC Property Used: Intersection of sets is associative A∩(B∩C)=(A∩B)∩C

Q: Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {e, f, h, j}, B =…

A: Ans - Given,            U = {a, b, c, d, e, f, g, h, i, j}           A = {e, f, h, j},  B = {d, f,…

Q: Let A and B be subsets of a universal set U. Give the theoretical definition of the following:…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-  parts for…

Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B).

A:

Q: Part 1: Proof that P(A N B) C P(A) N P(B). To prove part 1, select options from the list and put…

A:

Q: 6. Use a direct proof technique to prove the following theorems: The sets A, B, and C are arbitrary…

A: We have to prove C-A∪C-B=C-A∩B by direct proof technique.

Q: Let U be a universal set with subsets A and B such that n(U)=117, n(A)=60, n(B′)=68, n(A∩B)=15,…

A: Given,n(U)=117n(A)=60n(B')=68n(A∩B)=15n(B)=49and n(A∪B)=94

Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A…

A: A set is a collection of elements. The elements that make up a set can be any kind of mathematical…

Q: Give an example of two sets A and B which are homeomorphic, A is complete and B is not.

A:

Q: we defined the symmetric difference of sets A and B to be A AB = (A U B) – (A n B) = (A – B) U (B –…

A: The proof of associative law for symmetric difference is given as follows

Q: Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)are in A × B, find…

A: In AxB the first element will be from A and the second element will be from B So, x,y,z are in A And…

Q: Give an example of a set A such that there is a set B with B as the element of A but B is a subset…

A: Give an example of a set A such that there is a set B with B as the element of A but B is a subset…

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

A:

Q: Prove that for all sets A & B, (B-A) = A intersects B^c

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”.