A universal​ set, with​ n(U) = 30​, is partitioned into three​ subsets: A,​ B, and C.     If​ n(B) = 3​⋅n(A), and​ n(C) = 2​⋅n(B), find the number of elements in the subset A.     ​n(A) = nothing

Q: Consider the sets: A = {a, b, c, d, e, f, h, j}, B = {a, b, i}, C = {f, h} and U =…

A: Hey, since there are multiple questions posted, we will answer first question (1) with first three…

Q: How many unordered selections of three elements can be made from the set {a, b, c, d, e, f}?

A:

Q: Determine the number of subsets for the set T = {a, b, c}

A: topic- number of subsets number of subsets of set with n elements are 2n

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: 2. a. List all 3-combinations for the set {x1, x2, x3, X4, Xs}. Deduce the value of (,). b. List all…

A:

Q: 20

A:

Q: How many subsets does the set  F = {4, 5, 6, 7, 8}  have?

A: Given : F = 4, 5, 6, 7, 8

Q: 1) Define a subset.

A: To define a subset.

Q: Need help with part G,H,I

A:

Q: 2. If a set X has n elements, how many elements are in the power set P(X), we exclude the empty set…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: find a way to partition N into not two but infinitely many subsets with each subset containing…

A: All the natural numbers can be written in prime factorization form. The natural numbers are the set…

Q: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: Find the number of subsets that can be formed from a set containing 10 elements.

A:

Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

Q: Is there a formula to find the number of partitions in a set with n-elements?

A: Bell numbers, Bn, gives the number of partitions of a set with n elements It counts the number of…

Q: 2. How many 3 element subsets of the set {a, b, c, d, e, f, g, h, i} contain no vowels?

A:

Q: A(n) _____ is a collection of items called elements

A:

Q: How many unordered sets are possible that contain three objects chosen from seven?

A: Number of unordered sets that contain three objects chosen from seven = 7C3

Q: Consider the set C={Ø,{Ø},{Ø,{Ø}}}. How many elements are there in the power set P(C)? *

A:

Q: How many ways are there to select three unordered elements from a set with five elements when…

A: Given: Number of elements = 5 Number of unordered elements = 3 If repetition is allowed,…

Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: Show that the countable collection B = {(a,b) × (c, d)| a <b and c< d,

A:

Q: c a subset of the set of letters in the alphabet?

A: In set theory a set A is called a subset of a set B if all elements of A are also elements of B. It…

Q: List all the subsets of the set {I, D, E, A}

A: Answer -Find the list of all the subsets of the set {I, D, E, A}

Q: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

A:

Q: How many subsets does the set  F = {3, 4, 5, 6, 7} have?

A: No. of subsets in a set: The number of subsets in a set containing n elements is given by 2n. No. of…

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: List all the possible subsets of set G, where G = {-7,m,z}- %3D

A:

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: how many subsetsof one or more elemets can be formed from a set containing 12 elements?

A: Use concept of power set

Q: Determine the number of distinct proper subsets for the given set {c, a, v, e}.

A:

Q: How many elements does the successor of a set with n elements have?

A: Successor of the set, A is formed by adding an element {A} to the set. So, successor of A will be A…

Q: partition of Z into four subsets.

A:

Q: How many subsets of a set with 64 elements have more than two elements

A:

Q: Select the regions that correspond to the set AN BNC°.

A:

Q: How many unordered sets are there of two items chosen from eight?

A: To find unordered sets of two items chosen from eight. Number of unordered sets r chosen from n is…

Q: How many subsets is obtained from a set with 5 elements?

A: Given n=5

Q: How many unordered sets are there of two items chosen from four? ?sets

A: We have to find number of unordered sets of two items chosen from four items.

Q: Give the inclusion – exclusion formula for four sets where A U B U C U D in terms of sizes of in

A:

Q: 3. Find the number of subsets for set containing 3 elements.

A: Given set  containing 3 element

Q: How many elements are in the set {0, {0}}?

A:

Q: How many unordered sets are there of four items chosen from six? sets

A:

Q: Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are…

A:

Q: Show that if A is a countable set, and B CA is infinite, then B is countable. [Hint: How could we…

A: To prove that  If A is a countable set and B is a subset or equals to A is infinite then B is…

Q: Let S be a set of n elements. Find the number of distinct subsets of S.

A: Given: Let S be a set of n elements.

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If…

A: To determine the number of elements in each subset in the partition.

Q: How many subsets of a set with 50 elements have more than one element?

A: Introduction:  Here we need to find how number of subsets have more than 1 element. Given:…

Q: 10. If a set has 255 proper subsets, how many elements are there? Why?

A: