(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…

A:

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: Can a set and its complement be both dense in R? Can a set and its complement be both nowhere dense…

A:

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: 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: By showing that each side is a subset of the other side, prove that A △ B = (A ∪ B) − (A ∩ B)

A:

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…

A:

Q: Prove that intersection of any class of convex subsets of N is convex?

A:

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: Try it #2 Suppose that f(x)dx = 5, Só f(x)dx =-3, S g(x)dx = –1, and ſ g(x)dx = 2. Find the…

A:

Q: Determine which of the following subsets of R are well-ordered

A: A well-ordered set is a partially ordered set in which every non-empty subset has a least…

Q: Is Q x Z a closed subset of R2? An open subset of R²?

A: Since  is dense in , it is possible to find a sequence in which converges to . But,  not belongs to…

Q: Prove that the set X= { 2,6,10,14,....} is countable Note: no handwritten

A: Prove that: The set X= { 2,6,10,14,....} is countable

Q: Let A = {2n : n e N}, and B = {n E Z : n² is even}. Neither set is a subset of the other. O AC B. O…

A:

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

A:

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

A:

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: |(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: 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: Let S = {1,2,...,100} and A = {1,2, ...,10} and B = {41,42, ...,50}. What is the number of subsets…

A: We have a set S and two subjects A and B of S such that                S={1,2,3,......,100}   ,…

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: 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: 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: Construct an example of a subset B of p({a, b, c, d}) such that (B, C) is a totally ordered set.

A:

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.