Let X (a, b, c, d} and T = {X, , {a,b}, {c,d}}, then * O Every open subset of X is clopen O An open proper subset of X cannot be clopen O None of the choices O An open proper subset of X may be clopen and may be not.

Q: Let A be the set A = {1, 2, 3, 4) and let B be the set B = {5, 6, 7, 8). What is an element in B x…

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Q: if A ={x,{y},1,2,3,{2,3},{3}}      {} a proper subset of A      true or false

A: The problem is concerned with the nature of the empty set. The specific question is whether the…

Q: Let S be a set. For every subset A of S we denote by A the complement of A in S. Show that for all…

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Q: Which of the following sentence about the set A = 22⁰ is true? Ø, {0}, {{0}} are subsets of A 0, {0}…

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Q: Let A=(1, 2,3,4,5,6,7,8,9,10,11,12) how many different non-empty subsets are there in set A

A: Given,            A=(1, 2,3,4,5,6,7,8,9,10,11,12) We have to determine the number of different…

Q: Do A = {1,2,3, 4,...} and B = {-1,0,1,2, 3, 4, ...}have the same cardinality? O No because elements…

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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: Q5 Minimal Every partially ordered set has a minimal element. O True O False

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6,…

A: It is given that the universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.If A = {1, 2, 3, 4, 5} and…

Q: An indexed family of sets (Ahess said te be a cover of a set X tand only i X CUEIA Use this idea to…

A: Let C and D be two different indexed family of sets Ci and Dj. Then C=Ci:i∈ID=Dj:j∈J Suppose C and D…

Q: For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅. Let the universal set U be {1,…

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Q: Given a universal set U for a set X , if AC X , then (U – X) n A = Ø

A: Given a universal set U for a set X and A⊆X We shall prove it by contradiction method. Let us assume…

Q: Let U={1,2,3,4,5,6} be the universal set and A-{2,4,6}. Then the power set of the complement of U…

A: Given that  U={1,2,3,4,5,6} and A={2,4,6} To find The power set of the complement of U.

Q: Sets A, B, and C are subsets of the universal set U. These sets are defined as follows. U= {1, 2, 3,…

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Q: Let sets A and B be defined as follows. A-(-29,-28,-27, -26,-25,-24,-23,-22) B is the set of even…

A: Set A is given as, A = {-29, -28, -27, -26, -25, -24, -23, -22}.

Q: Let A = {1, 2, 3, 4, ..., 20}. What is the cardinality of the power set of A, P(A)?   Fill in the…

A: Cardinality of Set --: The Cardinality of a set is the total number of unique elements in the set.…

Q: Invent an interesting set A with AC {a, b, c, d, e, ..., z} and |A|≥ 6 and another interesting set B…

A: As per our guideline, we are supposed to solve only first three subparts. Kindly repost other…

Q: 7. Let Fa be a closed set for k=1,2,..., n. Show that Fk is closed. (Show that a fin and n 1 k=1

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Q: The universal set U is defined as the set of positive integers less than 10. The subsets A and B are…

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Q: A={ y ∣ y ∈ N and 305< y ≤ 335} A has      subsets.  A has              proper subsets.

A: We have, A={ y ∣ y ∈ N and 305&lt; y ≤ 335} Let A and B be two sets. We say that A is a subset of B…

Q: Let X = {a, b, c, d} and T = { X, þ, {a,b}, {a,b,c}}, then * An open proper subset of X may be…

A: Given that the set X = { a,b,c}

Q: Which of the following pairs of sets is a disjoint set? O (1,2,3,4) and (x x is a natural number and…

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

A: See the detailed solution below.

Q: If a finite set A equals the union of k subsets A1, A2,..., Ak, then the number of elements in A…

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Q: Given a finite set S, find all possible values of |S] so that the set {(a, b) | (a E S) A (b e S) ^…

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Q: Prove T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set

A: We have to prove the following -   T={ …,-56,-42,-28,-14,0,14,28,42,…} is a countable set.

Q: If S is a relation from a non-empty set A to a nonempty set B ther OS=AUB S = An B S≤AX B O S=AxB

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Q: Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B…

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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: Show that the set W of all whole numbers, W = {0, 1, 2, 3, . . 3, and N = 11, 2, 3, 4, . . 3 are…

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Q: For any set S if a*b = b*a, Va, b e S then * is said to be on S. (A) closed (B) associative (C)…

A: (a) For any set S if a*b∈S , ∀a, b ∈S , then *is closed on S   (b) For any set S if a*(b*c) =…

Q: Which of the following is NOT a finite set? * O A set of vowels. O {x:xE N, 1<x < 5} O (x:xe Z} O A…

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Q: Suppose A is a set for which |A| = 12. How many 5-element subsets of A are %3D there? (the number of…

A: Here given   A is set for which |A| = 12  So here no of elements in set A = 12

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”.