Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B are subsets of S and AcB is

Q: Prove for all sets of A, B, that P(A) U P(B) is a subset of P(AUB).

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Q: Let A be a set. Prove that S = 0. SEP(A)

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Q: 2. Is there a set A that satisfies A = {A}? If yes, exhibit one such. If not, Why not exactly?

A: No, there is no set A that satisfies A={A}. Let A is an empty set, i.e.  A=  or  A=ϕ, in which…

Q: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

Q: Let B be a set and {A: aeA} be an arbitrary family of sets. Then BUn A) = %3D

A: Answer

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: How do I write a set T such that S is an element of T and a proper subset of T?

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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: Assume that the set S has 14 elements. How many subsets of S have at most 4 elements

A: At most 4 means 4 or less.  Let us denote X=number of elements

Q: Let A be the set of letters of the alphabet between g and m. Express A in roster form and then in…

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Q: Write the following set in roster form: A={x:x is any two elements that belong to natural number…

A: Just observe step by step, we'll see a pattern.

Q: Suppore that A and B aru Awre set such that (AI= IB1 Show that %3D (P(A), P(B) denote the pouser…

A: We used the concept that if a set contains n elements then it power set contains 2n elements .

Q: 6. Every finite set in R is compact. Why?

A: The given question is related to real analysis. We have to show that every finite set in ℝ is…

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: Let U be universal set of all the students of Class X of a coeducational school and A be the set of…

A: In a coeducational school, there can be only boys and girls in school. Since, A is the set of all…

Q: Elements that are in the universal set but not in the set A, are members of the set called, of A.…

A: Universal set : Any set that contains all the sets is called Universal set Subset:  All the elements…

Q: (3) S° is the largest open set in M that contained in S.

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

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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: Prove that if A1, A2, ..., A, are any n > 2 sets, then A NA2 N …… A„ = A¡ UA2 U.…UA..

A: We will  prove the given statement using mathematical induction method.

Q: Let A and B be subsets of a universal set U, Prove that ACB if and only if B C A.

A: By definition, B′⊂A′ implies exactly two things: Every element of B’ is in A’ There exists an…

Q: Show that if A is an infinite set, then whenever B is a set, AUB is also an infinite set.

A: we have to prove that AUB is infinite set.  Since, given A is infinite set. since we know that…

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: Suppose that X and Y are sets such that the power set of Y is a subset of the power set of X. Does…

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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: The empty set o is open set ylgn O İhi O

A: See the detailed solution below.

Q: Assume that the set S has 13 elements. How many subsets of S have at most 4 elements?

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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: Let U be the universal set consisting of all positive even numbers. Let A be the subset of U…

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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: If A is set of all vowels in alphabets.Then number of subsets of A is

A: Given: A contains all vowels  So, A = a, e, i , o , u Number of elements in A = 5

Q: Let A be a finit set and let |p(A)|=n. Let B = A U {x} for some x∉B, How many subsets does B have…

A: Let A be a finite set with m elements Then number of elements in p(A) has 2melements Given p(A) =…

Q: Let the Universal Set, S, have 78 elements. A and Bare subsets of S. Set A contains 44 elements and…

A: Given data: The numbers of elements in the universal set are n(S)=78. The numbers of elements in the…

Q: Prove that if A is a set then so is {A} but do NOT use an argument that involves stages explicitly.

A: 3 Given A is any set. We have to prove that A is also a set. Since, A is any set Then as every set…

Q: 6. Give an example of a set S which is (i) bounded above but not bounded below, (ii) bounded below…

A: (i). Let  S = { ..., -5, - 4, - 3, - 2, - 1 }

Q: Let Ω be a set and A = {A ⊂ Ω : A is finite or Ac is finite }

A: given that Ω is a set and also given A ⊂Ω if Ω contains n elements  then A contains (n-1) elements…

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: 3. Prove that if A is a set then so is {A} but do NOT use an argument that involves stages…

A: Let A is any set then as every set is a subset of itself then, A⊆A⇒A∈PA⇒A∈PPA

Q: Let A,B be sets. Prove that AAB = if and only if A= B

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Q: 4. Prove that the set Z is a closed set in R.

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Q: The sets A and B have 6 and 9 elements respectively, such that A is proper subset B , then the total…

A: Given that set A and set B have 6 and 9 respectively. Now that A is a proper subset of B which means…

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: The cardinality of a finite set A, denoted by Al, can provide the of A as equal to 21A

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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: Let A1, · · · , An be countably infinite sets. Prove that A1 × A2 × · · · × An is countably…

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Q: For any set AcR, A is a Borel set.

A: Hi! As per norms, we will be answering the first question. IF you need an answer to others then…