a. Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and Z? How are X, Y, and Z related?

Q: prove that any set S subset of {1,2,,...100} with |S|=26 contains at least one odd number or it…

A: We have a subset S of {1,2,.......,100} with |S| = 26. We have to prove that S contains at least one…

Q: (Assume that in a university with 1000 students. 200 students are taking a course in mathematics,…

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Q: (a) In how many can the set {1; 2; ........; 16} be partitioned such that each part contains 2…

A: (a) Definition : Partition problem is to determine whether a given set can be partitioned into two…

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters codes can be…

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Q: 1) How many distinct subsets of {i} are there? (2) How many distinct subsets of {f,b,o,x} are…

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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: A(n) _______ is an ordered arrangement ofr objects chosen from n objects.

A: We fill the blank space as

Q: c) How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at…

A: Given the set of numbers 1,2,3,4,5,6,7,8 To find how many numbers must be selected from the set to…

Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,…

A: We know that, Hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…

Q: Let A=( a, e, i, o, u, ) a) How many proper subsets will A have? b) How many 3-elements subsets will…

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Q: 9. How many 8 element subsets are there in P({a, b, c, d, e, f, g, h, i, j, k, 1, m, n, 0, p})? 10.…

A: We have give a set of 16 elements. We have to get how many subsets which consists 8 elements.

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

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Q: Suppose A₁, A2, ..., A30 are thirty sets each having 5 elements and B₁, B₂, ..., B₁ are n sets each…

A: Given that A1, A2, . . ., A30 are thirty sets each having 5 elements and B1, B2, . . ., Bn  are 'n'…

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

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Q: (a) In how many different ways can the letters of the word combine be arranged? (b) In how many…

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Q: How many positive integers between 100 and 999 inclusive   d) are not divisible by either 3 or 4?…

A: The set: A∪B contains all the elements that are present in set A or B. The set A-B contains all the…

Q: Let A = {small, medium, large}, B = {red, magenta}, and C = {triangle, square}. List the elements of…

A: Solution: The objective is to list the all elements in BxC

Q: Number theory

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Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

A: Factorial Rule: The total number of ways n different objects can be arranged where the order of the…

Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

A:

Q: How many ways are there to arrange the letters m, n, o, p, and q such that neither m nor n is…

A: There are 5 letters in m, n, o, p, and q. We can arrange them in 5!= 120 ways   If m is followed…

Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

A:

Q: Consider lists made from L, a, T, e, X, with repetitions allowed. How many 4-lists are there in…

A: Please refer to the image below.

Q: A. How many 3-digit numbers can be formed from the set of decimal digits if the numbers formed are…

A: Answer is given below:

Q: Let A = ,2,3,45,6,73 How many subsets ot Contriin d) How many anly even numbers? subsets. ot A…

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Q: From the letters {A, B, C, D, E, F. G}, how :many 3-distinct-letters codes can be (a) generated? (b)…

A: a) 7C3 distinct codes can be generated by {A,B,C,D,E,F,G} which is equal to 21

Q: Suppose that in a certain state, all automobile license plates have three uppercase letters followed…

A: There are 26 letters [A-Z] and 10 digits [0-9] d) If the letters and digits are distinct then we can…

Q: Consider 4 digit numbers with each digit from the set {1,2,3,4,5,6,7,8,9} a) How many such numbers…

A: Solution

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: If A (5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; wheren is total number of distinct…

A: Consider two sets A and B. Then the union of these two sets contain all the elements in both A and…

Q: Let S(a, b) = {na + mb : n, m ∈ Z}. For any a and b in Z, not both zero, the set S(a,b) is precisely…

A: Take the set S={ax+by&gt;0:x,y∈Z} Without loss of generality, assume that a&lt;b. Then b−a&gt;0 is…

Q: How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed with…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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…

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Q: Let A = {small, medium, large}, B = {yellow, orange}, and C = {triangle, round}. List the elements…

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Q: If k, n are postive integers, with k<n, how many subsets of [n] are also not subsets of [k]?

A: Given k and n are positive integers with k&lt;n

Q: Let X = {a, b, c}, Y = {a, c, b}, and Z = {a, b, b, c, c, c}. What are the elements of X, Y, and Z?…

A: It is known that the ordering of the elements in a set does not matter. If the elements of both sets…

Q: Is {2,2}={2, {2} }? How many elements are in the set {a,a,a,a,a}? {x€N|xis greater than 10 and x…

A: First we have to check 2,2=2,2. Here in set 2,2 2 is the element but in 2,2 2 and 2 are the…

Q: How many elements are contained in the set (1,5)\{1}? 03 04

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Q: Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,…

A:

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: Find the number of subsets of the set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} having 4 elements. * 340…

A: Find the number of subsets of the set 1,2,3,4,5,6,7,8,9,10,11 having 4 elements

Q: 2. (i) Show that given finitely many countable sets A1, A2,, An, the set A1 x A2 x .. x An is also…

A: A set A is said to be countable if its cardinality is same as the set of natural numbers ℕ. If A and…

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: i. How many three-digit phone prefixes that are used to represent a particular geographic area (such…

A: here, AS PER GUIDELINES  I HAVE CALCUALTED FIRST MAIN  QUESTION  HERE USE COMBINATION , TOTAL…

Q: Show that 1 (N, <) is well-ordered. 1 2 (Z, <) is not well-ordered. 3 (R, <) is not well-ordered.

A: Please send questions as different questions. We cannot do more than 3 at a time.   A relation ≤ on…

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.

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

A: