A multiset is a collection of objects, like a set, but that can contain an object more than once (though the order of the objects does not matter). For example {1, 1, 2, 2, 2, 4, 3} is a multiset of size 7. a. How many sets of size 5 can be made using the numeric digits {0, 1, 2, ..., 9}? b. How many multisets of size 5 can be made using the numerica digits {0, 1, 2, ..., 9}?

Q: You have 10 of each of the following type of objects: A, B, C, and D. The objects of each type are…

A: 1. There are total 40 different objects, 10 belonging to each of types A, B, C, and D- A1, A2, …,…

Q: Which of the following sets are close under MULTIPLICATION? Choose ALL that apply. I. The set of…

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Q: How many 4-digit number can be formed out of 1,2,3,4,5,7 and 8 if: a. There is no restriction. b.…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: We are making 8-letter words from the set of letters a, b, c, d, e, f ..., in such a way that we…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

Q: An ice cream shop provides the following types of add-ons: hot fudge, caramel, cherry, Reddi-whip,…

A: Consider the  add-ons ice-cream shop provides: Hot fudge,caramel,cherry,redid-whip,chopped…

Q: Let U = {3, 4, 5, 6, 7, 8, 9, 10},  A = {4, 6, 8},  B = {3, 4, 7, 10}, and C = {3, 5, 7} . Find the…

A: It is given, U= {3,4,5,6,7,8,9,10}.

Q: A multiset is a collection of objects, just like a set, but can contain an object more than once…

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Q: 3. Consider the set of numbers S that are multiples of three and larger than 10. Write S in roster…

A: S is the set of numbers multiple of 3 and larger than 10 In roster notation S={ 12 ,15 ,18,21,24…

Q: How many subsets does the set X = {r, s, t, 10, 20, 15} have? %3D

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Q: Suppose set A={1,2,3,...,50} is divided into exactly two disjoint, nonempty sets. For example, one…

A: My approach is the I break into 2 disjoint part and take cardinality(number of element) of every…

Q: Assume that there are 55 students: 28 who enjoy tennis, and 14 who enjoy neither tennis nor…

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Q: How many subsets are there of the set N = {9}?

A: Given,          The set is N=9We know that,         The number of subsets of a given set is 2n ;…

Q: Let  U = {7, 8, 9, 10, 11, 12, 13, 14, 15, 16},   A = {7, 9, 11, 13, 15},   B = {8, 10, 12, 14,…

A: Given the universal set is U=7, 8, 9, 10, 11, 12, 13, 14, 15, 16. The sets A, B and C are as…

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: If | A| = 2 and |B| = 6, what is |AU B|+|An B?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 30-35. Given L = {0, –2,2, –1,2,3, –4,1, –3} A = {-100, ... 99, 100, .. 201} B = {3,2,1,6,5,4] Write…

A: The given sets are:L=0,-2,2,-1,2,3,-4,1,-3A=-100, . . . , 99, 100, . . . , 201B=3,2,1,6,5,4We have…

Q: Find the mode(s) for this lists of numbers.

A: The mode of any list of numbers is the number that repeated most frequently. If there are two…

Q: Let A₁ = {1, 2, 3, 4, 5, 6}, A2 = {7, 8, 9, 10, 11, 12, 13} and {14, 15, 16, 17, 18, 19}. A3 = How…

A: Let A1=1, 2, 3, 4, 5, 6, A2=7, 8, 9, 10, 11, 12, 13 and A3=14, 15, 16, 17, 18, 19.   To Find: How…

Q: A shopkeeper takes 12 bags of coins to the bank. The bags contain the following numbers of coins:…

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Q: are true regarding permutation and combination? See image below for the statements. 1 - Permutation…

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Q: Give an example of a set of numbers that is: a. Closed under both addition and multiplication. b.…

A: a. Set of real numbers b. Set of odd natural  numbers c. Set of irrational numbers

Q: A universal set U with 66 elements has been partitioned into three subsets, A, B, and C. If B is 2…

A: We use the definition of the size of a set to find the number of elements in the set B. The size of…

Q: How many four-letter (unordered) sets are possible that use the letters q, u, a, k, e, s at most…

A: Introduction: The definition of the combination is "An arrangement of objects where the order of the…

Q: A universal set U with 48 elements has been partitioned into three subsets, A, B, and C. If B is 5…

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Q: 1. How many ways can you choose 4 numbers from the set p = {4, 6, 8, 10, 12} or 3 numbers from the…

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Q: Question: Given a set A={1,2,3,4,5} a. How many subsets do A have (Hint: all possible subsets) b.…

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Q: Let B = {dog, house, cheese, book, car, phone, egg, square}. How many subsets does B have? How many…

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Q: 1. A multiset is a collection of objects, just like a set, but can contain an object more than once…

A: (1). We want the multiset containing 5 elements and the elements are digits from 0 to 9. Now, one…

Q: How many 4-element subsets containing the letter A can be formed from the set {A, B, C, D, E, F, G}?…

A: Number of 4 elements subsets containing the letter A from the set {A,B,C,D,E,F,G} is equivalent to…

Q: 1. Given 10 numbers a1, a2,..., a10, from the set S of natural numbers S = {1,2,3,..., 100}. Prove…

A: One question at a time pls.....or 3 sub parts .....bartbley rules

Q: 6. Determine. 2r - 3x 4x SET A.

A: I have stated the used formula in the solution

Q: A set contains 7 elements.  How many subsets exist? Group of answer choices a. 49 subsets b. 14…

A: If set P is a subset of set Q, then it can be said that all elements of set P are in set Q. Fore…

Q: o Digits = {0, 1, 2, ...,9} o Letters = {A, B, C,..., X, Y, Z} %3D o How many valid passwords are…

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Q: Determine all numbers n belong to N with the property that the set: A = {n, n + 1, n + 2, n + 3, n +…

A: SOLUTION:

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”.