Consider an undirected graph G = (V, E). Recall that a set SV is an independent set of cardinality k in G if and only if |S| = k and Vu, v € S : {u, v} & E (that is, there is no edge between any two distinct vertices in S). True or false: Let S be an independent set in G of cardinality k. Then G is k- colourable. True False

Q: 13. Let X and Y be subsets of any finite, nonempty set. Give the properties of the relation where X…

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Q: 6. Determine whether each set is finite or infinite. If a set is finite, find the cardinality. Write…

A: Note : " As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: 6. Show that the span of this set is all of R?. {}}

A: Let S=v1,v2,...,vn be a set of vectors in a vector space V(F) . The vector space V is spanned by S,…

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A: To show that if P is a u,v-path in a 2-connected graph G, then G does not necessarily contain a…

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Q: Give examples of three relationships that show all possible combinations of minimum and maximum…

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Q: Consider the non empty sets A and B such that A and B have the same cardinality. Prove, for any set…

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Q: Let X be a set and P(X) its power set. Explain what it means that the cardinality of P(X) is…

A: It is required to explain the meaning and to prove that the cardinality of power set P(x), of X, is…

Q: Use graph to find  set. [1, 3) ∩ (0, 4)

A: Given set is  [1, 3) ∩ (0, 4) The graph of the given set is as shown

Q: The cardinality of the set P(R) is Select one: O a. less than |R| O b. equal to |R| O c. cannot be…

A: USING CANTOR'S THEORM ,WHICH STATES THAT THE CARDINALITY OF A SET IS STRICTLY LESS THAN THE…

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A: Introduction: Counting the number of items in a set, or its cardinality is a way to gauge its size.…

Q: Let A and B be any two sets. A binary relation from A to B is i. CAXB ii. SANB CAUB Non of these…

A: Firstly we define binary relation from set A to set B, and then conclude the answer.

Q: List all the possible subsets of set G, where G = {-7,m,z}- %3D

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Q: pigeon hole principle

A: Answer (1) E = { (u,v) , u, v ∈ V | person u and V have met each other}(2) degree of a vertex u of G…

Q: Find the cardinality of each of the following sets. a. A = {x:xe Z and x² = -9} b. B = {x:x € R and…

A: The given sets,(a) (b) (c) (d) The aim is to find the cardinality of each of the given sets.

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Q: A set F is called an Fo-set (or an Fo) if it is a countable union of closed sets. Likewise, a set G…

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Q: 1. We are given the sets S and V: S {Anne, Theo} V = {studies, runs, meditates} (a) Find the…

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Q: Prove that if a graph G does not contain either Por ging C₁ as an induced subgraph, then y(G) = 1.

A: Please find the attached answer.

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A: Use the graph to find [2,∞)∩(4,∞)

Q: Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show…

A: Here, {p1,p2,p3} is an affinely independent set. So, {p1,p2,p3} are linearly independent.

Q: 20 - Determine whether the relation with the directed graph shown is an equivalence relation ? a d

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Q: Suppose A, B, and C are sets with cardinalities |A| = 7, |B| = 5, and |C| = 3. Compute the…

A: Given problem:- Suppose A, B, and C are sets with cardinalities |A| = 7, |B| = 5 and |C| = 3 Compute…

Q: If R is a relation on a set A, the directed graph of R has an arrow from x to y if, and only if,…

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Q: List all the ordered pairs in the relation R= {(a, b) | gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.

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