k-Rainbow and independent k-rainbow domination of some special graphs Lemma : Let Hk,n (2 ≤ k

Q: 9. What is the set-builder equivalent of {0, 1, 2 }? 10. What is the set-roster equivalent of {x E…

A: Set: Set is any collection of objects or elements which may be numerical or non-numerical. Set…

Q: Lemma 1 Consider a node x with rank (number of children) d. Let y1, y2, ... Yd be those children in…

A: Given  y1, y2, ...... yd are children inthe order they were added to the tree.  We have to show that…

Q: 4. Write out the following sets, and give a formal proof that set-builder notation expression (as…

A: The set builder notation is given as, {x∈ℝ: x2=x} × {x∈ℕ : x2=x} As in the case of real numbers all…

Q: 37. Which of these three statements is/are not true? I: Every finite nonempty subset of R has a…

A: We shall answer all the parts and provide justification as to why a particular part is not true. In…

Q: Choose the response that correctly completes the following statements: • The graph of r = 4 in…

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Q: - Show that S¹ = {(x, y) = R²|x² + y² = 1} and D² = {(x, y) = R²|x² + y² ≤ 1} have the same…

A: To show that the unit circle and the closed unit disk  have the same cardinality, establish a…

Q: For any two non-negative integers x and y, let d(x, y) = x + y. Let x, y, z be any three…

A: See solution below

Q: (e) ((SNT)US) (f) U-S (called the complement of S) Given that the set S contains n elements, show…

A: To show that a set S with n elements has 2^n subsets, you can use the concept of the power set. The…

Q: 1. Prove: N × N is countable. 2. Prove: The Cartesian product of countable sets is countable. 3.…

A: Since you have posted multiple questions. But according to guideline, we will solve first question…

Q: 1. Find all regular points of the set : {x € Rª | 2(x1+x2+x3)³ +3(x1+x2+x3)² = 1, x²+x²+x²+x4 = 1}.

A: The given set is: x∈R4|2(x1+x2+x3)3+3(x1+x2+x3)3=1,x12+x22+x32+x4=1

Q: Let A= {k: k ∈ N, k ≤ 20}, B= {3k−1: k ∈ N}, and C= {2k+1: k ∈ N} 1. A INTERSECTION B INTERSECTION…

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Q: . Sketch the graph of the set defined by A x B where A is the closed interval [-2, 4] and B = {1, 3,…

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Q: How many nonisomorphic (free) trees are there with 4 vertices?

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

Q: Lemma 1 Consider a node x with rank (number of children) d. Let y1, Y2, ..., Yd be those children in…

A: Given x is a node with rank d. y1, y2, ...... yd be those children in the order they were added to…

Q: Let U = the set of all trees M(x) = "x is a Maple tree", E(x) = "x is an evergreen tree" %3D %3D…

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Q: Describe the following sets by roster method: Example (i) {x : x + 5x + 6 = 0, x e N} (iii) {x : 4x…

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Q: . Every vertex of a polyhedron is exposed

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Q: F and Hare sets of real numbers defined as follows. F = {ww≤ 4} H = {w|w>5} Write FUH and FnH using…

A: We can find the union and intersection of sets in the below steps.

Q: The set of natural numbers N satisfies the following three properties: (i) m, n E N → m+ n, m · n, m…

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Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

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Q: 3. True or False. Determine whether the given pairs of sets are equal. a. A = {2n + 1|n E W} ; B =…

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Q: 6. (a) Let A, B, be subsets of R. State the conditions which make the pair (A, B) Dedekind cut. (b)…

A: It is given that Let A, B be subsets of R.

Q: Plot Me(x), Hole), Mcvo M and Ulx).

A: Plot of the membership function μCx: Plot of the membership function μDx:

Q: (A) If A = {x E R: – 1<x< 2}, B = {x € R: 0 < x < 1}, C = {x € R: 1< x < 2}, The sketch the graph of…

A: That's easy, have a look.  Have a great day!!!

Q: Problem 7. A relation is defined on the set of positive integers N by n ~ m if either n divides m or…

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Q: (a) Find the value of x such that 61, = 133, (b) M and N are two intersecting sets. If n(M) = 20,…

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Q: (1.2.7)List all elements in the following sets. (a) T = {m € Z | m = 1 + (−1)¹ for some integer i}…

A: The sets are: (a) T=m∈Z | m=1+-1i for some integer i (b) U=r∈Z | 2≤r≤-2 (c) U=r∈Z | -2≤r≤2 To Do:…

Q: An independent set of a graph G is a subset I of the vertex set V such that no two vertices in I are…

A:

Q: 5. For example, fuzzy sets A and B are defined by the function : for 2 ≤x≤ 10 A(x) = 1-(|x-61/4) 0…

A: As per the question we are given two fuzzy logic sets A(x), B(x) and from that we have to find: The…

Q: T: Readiness Assessment In ABC, what is the length of BC ? Ay B A 10 12 O A. 169 оВ. 13 о с. 17 O D.…

A: We have to solve

Q: bute 80 identical pencils in a class consisting of 10 boys and 20 girls in such a way that each of…

A: Given:- Number of boys=10 Number of girls = 20 Number of Pencils=80

Q: Graph the set {x -3<x<2} on the number line. Then, write the set using interval notation.

A: Given, Graph the set {x|-3≤x≤2}

Q: Let k and n be positive integers. Let G be the graph with vertex set (n] such that u and e are…

A: Consider the given graph G whose vertex set is [n] and the vertices u and v are adjacent if and only…

Q: Suppose that a > 0 is a positive integer, and n > a. How many lattice paths are there from (0, 0) to…

A: According to the given information, suppose that a&gt;0 and n&gt;a. It is required to find the…

Q: If k k k = 2, and x = integer, which statement is NEVER true about x? %3D %3! es 4) A) x is 0 B) x…

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Q: Prove that the set B = {r € Q: 1² < 20 or r < 0o} is a cut.

A: In this question, we have to prove that the set,  B = x∈ℚ : x2 &lt; 2 or x &lt; 0 is a cut.

Q: 2. Consider S3 = the set of all permutations on the set [3]. You can find these 6 permutations in…

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