1) Define a subset.

Q: List all the subsets of {x, y, z, y}.

A:

Q: List all the subsets of the set                   { –1, 0, 1 }.

A: All subsets of {-1,0,1} is:

Q: {k}, {I, m, o}, {n, p}} of the set U = {k, I, m, n, o, p}. Give the

A: Solution is attached below.

Q: 2. Finite subsets of Rd are closed. Gap to fill in

A: Given statement is Finite subsets of ℝd are closed.

Q: define a set of which both {1,3,4} and {0,3,5} are subsets find such a set with the smallest…

A: We have to find the set with smallest possible number of elements which both {1,3,4} and {0,3,5} are…

Q: 9. Consider the 8-elements set A = {a, b, c, d, e, ƒ, g, h} . How many subsets of set A have 4…

A: Solution

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: 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: If set Z has 7 elements, how many subsets does it have?

A:

Q: .State all the subsets that apply to /2. Include an explanation supporting why v2 belongs in each…

A: Consider the given expression, 2 the value of the given expression will be, 2=1.4142135624 it can be…

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: Draw a Venn diagram with three overlapping circles for the three given sets. Label the contents of…

A: Venn Diagram for the problem involves the use of 3 overlapping circles for the sets So Venn diagram…

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: Set C is a set of states in the United States whose names start with the letter H in roster form

A: In this question we have to write a set C in roster form which contains states of United Stated…

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

A:

Q: what are subsets?

A: Let us consider two sets A and B.A is called subset of B if and only if B set have all elements of A…

Q: The set of elements that are members of set A or set B or of both sets is called the. of sets A and…

A: Note that, a set is a collection of objects. All the object that are clearly determined in a set are…

Q: A universal​ set, with​ n(U) = 30​, is partitioned into three​ subsets: A,​ B, and C.     If​ n(B) =…

A: we are given n(U) =30​, n(B) =3​⋅n(A), and​ n(C) =2​⋅n(B) also universal set is partitioned into…

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

A:

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: Does the set S = span M22?

A: The given set is S=1100, 0011, 1001, 0111. Note that the above set is linearly independent set.

Q: If A=(1,2,3,4,5.6,7), What is the number of nonempty subsets of A?

A:

Q: Find a set of smallest possible size that has both {3,4,7,8} and {1,5,6,9,10} as subsets.

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: If a set S has n > 3 elements, how many subsets of S have less than n – 1 elements?

A: Apply the simple logic of Permutation &amp; Combination.

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: Identify the set shown below as finite or infinite, {10, 11, 12, ..., 40} ..... OInfinite O Finite

A:

Q: 5. Show that a finite union of countable sets is countable.

A: The answer is given as follows :

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 subsets of a set with 21 elements

A: To determine the number of subsets of a set with 21 elements

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

A: Given n=5

Q: Give a set that is not closed under addition

A: In the question we have to give a set that is not closed under addition.

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

A: Given set  containing 3 element

Q: Suppose that set A has 17 elements, set B has 10 elements, and their union has 18 elements. If the…

A:

Q: Let S := {l, a, t, e, r, a, l}. How many subsets does S have?

A: Given: S = {l, a, t, e, r, a, l} Here, number of elements is n = 7.

Q: specify the set by roster distinct letters in the word (mathematics)

A: Given that

Q: find the subset of (E, B,T,*)

A:

Q: prove that the union of a countable set and an uncountable set is uncountable

A:

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: 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: Consider a set S = {A, B, a, b, c, d, 1, 2, 3, 4}.

A: As per guidelines, the handwritten answers are not acceptable. So, we will provide only typed…

Q: Is {A, B, C} a subset of the set of letters of the alphabet?

A: Subset is a set of which all elements are containd in another set.

Q: Define subsets and give a relevant example along with it.

A:

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: How many subsets of size 3 can one find in a set of size 5?

A: Hey, since there are multiple sub parts posted, we will answer the first question. If you want any…

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: