(4) How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all of A?

Q: prove that any set S subset of {1,2,,...100} with |S|=26 contains at least one odd number or it…

A: We have a subset S of {1,2,.......,100} with |S| = 26. We have to prove that S contains at least one…

Q: a) Let S={a, b, c}, and for each integer i= 0, 1, 2, 3, let S, be the set of all subsets of S that…

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Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

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: a. Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and…

A: # we are entitled to solve one question at a time. Please resubmit the other questions of you wish…

Q: Suppose that A and B are subsets of S. (a) Show that A ∩ B and A ∩ Bc are disjoint. (b) Express A as…

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Q: If A and B are partitions of [a,b] and ||A|| < ||B||. then ВСАФ B not subset of A A not subset of B…

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Q: True or false? A∩(B∪C)=(A∩B)∪(A∩C) You should determine this by building the Venn Diagram for each…

A: Given statement is A∩(B∪C)=(A∩B)∪(A∩C)

Q: Are   any   open   subsets   of   R   sequentially   compact?     Explain   why   or   why not

A: The objective of the question is to determine whether any open subsets of the set of real numbers…

Q: Give an example of a set that contains nine elements of which two are sets. List three Subsets of…

A: Let the set which contains 9 elements be, A=1,2,3,4,5,6,7,8,9

Q: Let A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }. Give an example of three sets, A1, A2, and A3, such that…

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Q: Which sets are compact? The union of [0, 1] and [2, 3]

A: Concepts introduction: Theorem (Heine-Borel Theorem): A subset S of R is compact if and only if S is…

Q: Suppose we have a set A={1, 2, 3, 4, 5, 6}. What is the partition of A into three parts? Make sure…

A: We can partition of set A as below

Q: 9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by…

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Q: If B1,..., Bn is a finite open cover of a compact set A, can the union B1 U... U Bn equal A exactly?…

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Q: Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.  a) A union B b) A intersection B c) The complement of…

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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: 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 = {0, {1, 2}, 3}. Make a list of all elements of A and a (separate) list of all the subsets of…

A: To solve the given question we use the defination of set and find the subset of the given set.

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: |(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: Consider the indexed collection {AnneN of sets given by An = {x € Z : |x| < 42 +n and x < 42/n} for…

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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 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: Use the pigeonhole principle to prove that any 6-element subset of {1,2,..., 10} contains a pair of…

A: This question from discrete mathematics and topic is pigenhole principle.

Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

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

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Q: Let A = {1, 2}. List all the subsets of A. Let B = {1, 2, 3}. List all the subse

A: 1. Let A=1,2find the subsets of A.2.Let B=1,2,3list the subsets of B which are not contained in A.

Q: Let set A = {a,r,t} a) list all the subsets of A b) State which of the subsets, if any, from part…

A: Topic- subsets  we are given a set A={a,r,t) any set is subset of A ,if all the elements in a set…

Q: Prove that a selection of 7 numbers from the set {1, 2, . . . , 11} contains numbers m and n such…

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Q: Is {1} proper subset of A  A={x,{y},1,2,3,{2,3},{3}}

A: A proper subset of a set A is a subset of A that is not equal to A.Or in other words, if B is a…

Q: Determine the number of distinct subsets for the given set {t, a, p, e, f, g}.

A: Given set {t, a, p, e, f, g} Since there is no. Of elements = 6 (say n)

Q: Write down four distinct elements of the set {z ∈ C : z − z ̄ = 2i}.

A: The given set is z∈ℂ:z-z=2i We have to find the four distinct element of the given set.