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

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

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

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Given information- We have given that the set S has 7 elements. We have to find the number of subset…

Q: Let S be a set with |S|=6 . In how many ways can we partition the set S into three non-empty parts?

A: Answer:   3   Here    |S| = 6 So there are total 11 possible partitions which are 6 5+1 4+2 3+3…

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: Choose any that is a subset of the set S={10, Ø,{{ Ø}}} 0{0} {(Ø), 10) 0 {{0}}

A: Solution

Q: How many proper subsets does the set W, containing the days of the week, have? W={Monday, Tuesday,…

A:

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

A: Solution :-

Q: 7. Show that if S x T is a closed subset of R?, then S and T are closed subsets of R.

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: 1. Let A, B and C be the subsets of U. Then prove that (A – B) - (B - C) = A-B by using laws of sets

A: Using properties of set theory

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: How many sets of are in 2-½?

A:

Q: List the elements of the following set: S = {x|x ∈ ℤ, x is odd, 16 < x2 ≤ 160}

A: We are given the set, S = {x|x ∈ ℤ, x is odd, 16 < x2 ≤ 160}. Here, we need to list all the…

Q: Let A and B be subsets of a universal set U and suppose n (U) = 275, n(A) 100, п (В) = 70, п (An B)…

A: If A is subset of universal set U, then n( Ac ) =n(U)-n(A).

Q: List all the subsets of the set A = {a, b, c, d}

A:

Q: (3) S° is the largest open set in M that contained in S.

A:

Q: about the three subsets X1, X2, and X3 that partition a set X, except assume that the number of…

A: Let there are x elements in X2. So there are 6x elements in X1. There are 3x elements in X3. Given…

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

A:

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

A:

Q: Show that if A, B, and C are sets, then A n Bn C = A U BUC a) by showing each side is a subset of…

A:

Q: Let R = Zg, and let N = R³. Determine whether or not X = {(4, 5, 4), (4, 5, 2), (2, 2, 3)} is a free…

A: It is given that,  R = ℤ8  and  N = R3. We have to determine that whether the set,  X = 4, 5, 4, 4,…

Q: Let A = {1, 2, 3, 4, 5}. How many subsets of A have no more than 3 elements?

A:

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) ^…

A:

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: If H={1,2,3} and P={2,3,5}. How many proper subsets does H∩P have? (Don’t forget the empty set!)

A: If the cardinality of a set is n then a number of subsets of S will be 2n - 1.

Q: Assume that the set S has 7 elements. How many subsets of S have at most 3 elements?

A: Consider that  the set S has 7 elements. The subsets can have 3 elements, 2 elements, 1 element, and…

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: 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: Use set-roster notation to indicate the elements in the following set: S= {n € Z | -3 < n< 1}

A:

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

Q: a)​ n(A ∪ ​B) ​b) nA′ ∪ C ​c)

A:

Q: For A = {a, b, c}, let (24, S) be a partially ordered set. Find (i) an upper bound, (ii) a lower…

A:

Q: 5. Find the power set of each of these sets, where a and b are distinct elements. a. {a}

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: Enumerate

A: The set S contains 5 elements, Number of subset = 25 = 32

Q: 15 Assume that set S has 11 elements. How many subsets of S have at most 2 elements?

A: Solution : A set S has 11 elements We want to find subset of S have at most 2 elements

Q: Enumerate all the subsets of each of the following sets. A = {1, 2, 3, 4, 5, 6}

A:

Q: A set has 9 elements. How many subsets of S are there with at most 2 elements?

A: Given,            A set has 9 elements. Subsets of S are there with at most 2 elements.

Q: If set K is such that n(K) = 3, then set K has 6 subsets

A:

Q: Let A = {t, u, v, w}, and let s, be the set of all subsets of A that do not contain w, and S, the…

A: The set A=t,u,v,wS1 be the set of all subsets of A that do not contain wS2 be the set of all subsets…

Q: Let the universal set U be a standard deck of 52 playing cards. Let E be the set of all even…

A: The intersection of two or more given sets is the set of elements that are common to each of the…

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: Let U = {6, 7, 8, 9, 10, 11, 12}, and A = {6, 7, 8, 9}. List all the members of the given set.  Ā

A: The Universal set U is defined as U = {6, 7, 8, 9, 10, 11, 12}.

Q: Choose any that is a subset of the set S=(10, Ø,{Ø}}} O(Ø) a {(Ø), 10)

A:

Q: Suppose A is a set with 7 elements. Answer the following questions: 1. How many subsets of exactly…

A: Given, A is a set with 7 elements In a set the order doesnot matter so here we use combinations.

Q: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} Use the roster method to list the elements in the set A. A=

A: Given: A={ z ∣ z ∈ N and 195 ≤ z ≤ 201} The roster form is given by

Q: Let S = {a, b,f,g, i, k, m, q, t} . (1) How many subset of S have exactly 3 elements? (2) How many…

A: We have to find no. Of subset as per given question.

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”.