The intersection of two fuzzy sets S and T is the fuzzy set S ∩ T, where the degree of membership of an element in S ∩ T is the minimum of the degrees of membership of this element in S and in T. Find the fuzzy set F ∩ R of rich and famous people.

Q: Consider the following statement. (Assume that all sets are subsets of a universal set U.) For all…

A: Please see the answer below.

Q: Let A, B and C be overlapping sets, verify following by using Venn diagram and membership table ((An…

A: Consider the provided question,

Q: Prove that if A and B are sets, then P(A) U P (B) C P(AUB).

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Q: Consider the set S:= {(z, y, 2) | 2. y.2 E {0, 1}} which is expressed in set-builder notation.…

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Q: Let C, D be subsets of a set U. By proving two inclusions, show that (CC n D) U (C n D) = D where Ce…

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Q: The set of elements common to both set A and set B is called the______ of sets A and B, and is…

A:

Q: If A and B are non-empty sets defined on a universal set U. and An B = Ø, then A\B is equal to

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Q: Prove that if A is transitive set, then A+ is also a transitive set.

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

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Q: Find a counterexample to show that the statement is false. Assume all sets are subsets of a…

A: The solution is as shown below

Q: Let A, B, and C be subsets of a universal set U. Suppose n(U) = 80, n(A) = 20, n(A∩B) = 5, n(C) =…

A: Given, n(A) = 20, n(A∩B) = 5, n(A u B)= 40

Q: Let A, B and C be the subsets of U. Then prove that (A UB) – C = (A – C) U(B – C) by using laws of…

A: I have just used the law of sets

Q: Use the pick-a-point method to show that if A and B are subsets of some universal set U, then A ∪ (B…

A:

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

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Q: 2. Recall that for two sets A, B, the Cartesian product of A and B is the set Ax B = {(a,b) : a € A…

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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: Let A, B, and C be sets. Does A- B= A –C imply B = C? If so, prove it. If not, give a…

A: Let A, B and C are sets. We have to find out that A-B = A- C implies B = C or not If not then we…

Q: Let A, B be any sets with ACB. Then * O None of these O IP(A×B)|<|P(B×B)| O IP(A×B)|=|P(B×B)| O…

A: Power Set: If A is any set, the collection of all its subsets is another set is called the power set…

Q: Let A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 150, n(B) = 90, and n(A ∩…

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Q: Show that if A, B, and C are sets, then A n Bn C = A U BUC a) by showing each side is a subset of…

A:

Q: |(A ∪ B)\(C ∪ D)|

A: We have to give a formula for |(A ∪ B)\(C ∪ D)| in terms of the sizes of the four sets A, B, C, D…

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

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Q: (d).Show that the derived set E′E′ of any set EE is closed.

A: To show that derived set E′ of any set E is closed.

Q: Suppose that A is a set and {Bn}nɛ1 is an indexed family of sets. Prove that A - U B, = N(A – B„,).…

A: Suppose that A is a set and Bnn∈I is an indexed family of sets. Then we have to prove that…

Q: Let C, D be subsets of a set U. By proving two inclusions, show that (C° n D) U (Cn D)= D where Ce…

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Q: , and C be subsets of a universal set U and suppose n(U) = 200, n(A) = 26, n(B) = 28, n(C) = 32, n(A…

A: Let A, B and C be the subsets of a universal set U . nU=200, nA=26,n(B) = 28, n(C) = 32, n(A ∩ B) =…

Q: Let C be a nonempty subset of a bounded set D. Why does inf C and sup C exist? Show that (c) inf D ≤…

A:

Q: 1. Let A, B, and C be sets. Does A - B = A – C imply B = C? If so, prove it. If not, give a…

A: This question is related to Set theory, We will solve it using given information.

Q: Let the universal set be the 26 letters in the English alphabet, and let A = {a, b, c, d}, B={c, d,…

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Q: Consider the following statement. (Assume that all sets are subsets of a universal set U.) For all…

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Q: Suppose A, B, and C are sets, A. Prove that: Ax (Bn C) = (A × B) n (A × C) %3D Using Membership…

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Q: a) the set of sophomores taking discrete mathematics in your school b) the set of sophomores at…

A: Given: It is given that suppose that A is the set of sophomores at your school and B is the set of…

Q: show that empty set, X is an element of S intersection T in topology

A: Here We have to show that empty set must be in S∩T where S and T are topology on set X.

Q: Draw a Venn diagram for the symmetric difference of the sets A and B.

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Q: Let A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and s, the…

A: We are given with multiple sub parts since our guideline is solve first three subparts.

Q: Let A, B, and C be subsets of a universal set U and suppose n(U) = 150, n(A) = 27, n(B) = 29, n(C) =…

A: A set is the mathematical model for a collection of different things; a set contains elements or…

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: We have given the following n(U) = 300, n(A) = 150, n(B) = 120, and n(A ∩ B) = 60.

Q: let X={a,b,c} Construct two topologies for the set that have at least 4 open and that are…

A: Given that X=a,b,c. To construct two topologies that have at least four open sets. We know that in…

Q: Let A, B, and C be sets. Does A – C = B – C imply A = B? If so, prove it. If not, give a…

A: We have to give a counter example for  A – C = B – C imply A = B.

Q: Let A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and S, the…

A: The set A=t,u,v,wS1 be the set of all subsets of A that do not contain wS2 be the set of all subsets…

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: Let A, B be any sets with BCA. Then |P(B×B)[s|P(A×B)| O IP(AxB)|s|P(B×B)| O IP(AxB)|=|P(B×B)| O None…

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Q: Prove that if A, B.C are subsets of a universal set U, then AU(BnC) C (AUB)n(AUC)

A: use the basic property of subset and set theory.

Q: Determine whether the set S = {1, x², 9 + x²} spans P2. %3D O S spans P2. O s does not

A: Introduction: Vectors' span, It is the collection of all linear combinations of a number of vectors.…

Q: Let A, B be any sets with ACB. Then O None of these O IP(B×B)|s|P(A×B)| O IP(A×B)|s|P(B×B)| O…

A: Cardinality of a power set

Q: b) Prove the second De Morgan law in by showing that if A and B are sets, then AUB=ANB i) by showing…

A:

Q: Show that the union of two sets, each of measure zero, has measure zero

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”.