A set S has 8 elements, how many subsets A ⊆ S are there such that: (a) A has at most 3 elements (b) A has at least 5 elements. (Hint: You do not need to calculate anything!)

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

A:

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: 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: Set A contains 19 elements, set B contains 22 elements, and 6 elements are common to sets A and B.…

A: A set is a well-defined collection of objects, these objects are called the elements of the sets.…

Q: 12. Let B be a subset of A. Let |A| = n and |B| = k. What is the number of subsets of A whose…

A: Given B⊂A. A=n and B=k Now if any subset C of A has 3 elements in intersection with B then C≥3 For…

Q: a. How many students prefer Canvas only? b. How many students prefer at most one platform?

A: We shall find out the answer of the given questions From the table provided.

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: 2. Consider the collections C = {penny, nickel, dime, quarter} D = {penny, nickel, nickel, dime,…

A: (a) The number of elements in collection C is 4 and the number of elements in the collection D are…

Q: A study was done to determine the efficacy of three different drugs-A. B. and C-in relieving…

A:

Q: How many subsets of S do not contain any upper case letters?

A: given set S=A,B,a,b,c,d,1,2,3,4 claim- to find how many subsets of Sdo not contain any upper case…

Q: Suppose we want to choose 7 objects, without replacement, from 9 distinct objects. (a) How many ways…

A:

Q: (a) How many ways are there to distribute seven identical apples and six identical pears to three…

A: Given: To distribute seven distinct apples and six distinct pears.

Q: Given that set A has 41 elements and set B has 22 elements, determine each of the following. (a) The…

A: Set A : 41 elements  Set B : 22 elements

Q: Consider a bag containing five red marbles, two green ones, one transparent one, four yellow ones,…

A:

Q: b . What is the minimum number of cards that must be drawn from an ordinary deck of cards to…

A: b)i) There are 13 ranks. [J,K,Q,A,2,3,4,5,6,7,8,9,10] If we have 2 cards from each rank , then we…

Q: e) True or False: If 25 oranges are placed into 22 baskets, then at least one basket must contain at…

A:

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

A:

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

A:

Q: Suppose A is a set with 6 elements. Answer the following questions:   1. How many subsets of…

A: In a set the order does not matter. So we can use the combination method. 1) We can pick 4 elements…

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: A set contains 7 distinct elements. How many subsets can be formed from the elements of S that…

A: Use combination formula

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

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 & Combination.

Q: 1) Each student is classified as a member of one of the following classes: Freshman, Sophomore,…

A: the pigeonhole principle states that if {\displaystyle n}n items are put into m containers, with…

Q: Some nonempty set has 211, at most two-element subsets. how many elements does this set have?

A: The number of ways, to select r number of different objects, from n number of different objects, can…

Q: 20 The set [20] contains = = 15504 five-element subsets. How many of them contain more odd elements…

A: There are 15504 five element subsets. The set of 20 numbers contains 10 odd and 10 even numbers. If…

Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

Q: Suppose we want to Choose a aobjects, without replacement, From the s objects pencil, eroser, desk,…

A: There are 5 objects that is pencil, eraser, desk, chair, lamp Two objects are selected without…

Q: How many ways are there to form a subset of (n| of size k with the property that each selected…

A: Let us define some events   A:- box 1 is selected B:- box 2 is selected E:- Yellow ball is selected

Q: A restaurant offers a special pizza with any 6 toppings. If the restaurant has 11 topping from which…

A:

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: 2. Let S be the set [9] [1.2. (a) How many derangements 9). has the set S?

A: S = [9] = {1, 2, 3, 4... 9}  There are 9 elements  Hence, number of dearrangements = !9  =(9!)(1/2!…

Q: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

A: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

Q: (a) How many 4-permutations are there of a set of six objects? (b) How many 2-permutations are there…

A:

Q: Each of the 20 students learn exactly two of the three languages: English, French and German. 80% of…

A: Total number of students= 20 Number of students learn English= 80% of 20 = (80÷100)*20= 16 Number of…

Q: (a) How many 4-permutations are there of a set of five objects? (b) How many 2-permutations are…

A:

Q: A restaurant offers a special pizza with any 5 toppings. If the restaurant has 10 topping from which…

A: this is a combination problemtotal number of topping=10number of topping can be chosen=5so number of…

Q: Let D be a standard deck of cards, let SV = {A♡, K♡,Q♡, JO}. a) List all the subsets of S♡ that…

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: How many strings of eight English letters are there a) that contain no vowels, if letters can be…

A: Given the question that, How many strings of eight English letters are there- a) that…

Q: Television and radio stations use four call letters starting with W or​ K, such as WXYZ or KRLD.…

A: the total number of alphabets between A to P is 16.

Q: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: Show that                                n                    n                     (            )…

A: To interpret (hence prove) the given equality of the two binomial coefficients, using set theory

Q: A given large basket can contain 70 pieces of fruit consisting of apples, bananas, kiwifruit,…

A:

Q: About the subsets A⊂B⊂CA⊂B⊂C of a universal set UU, except assume that n(A)=5n(A)=5 and…

A: Question concerns the number of different possibilities for the subset B under the given conditions

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”.