1. For the following, each relation R is defined on the set A. Determine if R is a tree, root. a) A= {a, b, c, d, e}; R = {(a, d), (b, c), (c, a), (d, e)}

Q: Draw the directed graph of the relation R = {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} X=123 43

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Q: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

Q: Let d be the highest degree of any vertex in a tree T, and let l be the number of leaves of T. What…

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Q: Prove that for any set relation R (we did not pick it to be "on" any particular set) R* =N{Q:RC Q^ Q…

A: Given that any set relation R.

Q: If A (1,3.4) and R is a relation defined on A as: R = {(r.y) E Ax A:r-y is odd ), Then relation Ron…

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Q: Draw the direction of the graph that represents the relations.

A: We need to draw the directed graph which is represented by the given relation,…

Q: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17}…

A: The domain of the equivalence relation D is the set S: S = {7, 2, 13, 44, 56, 34, 99, 31, 4, 17} For…

Q: 4. Consider the relation R = {(-3, –3), (-3, –5), (-5, –7), (–7, –3), (–7, –7)} on the set А 3D {-1,…

A: We have to  (a) To Draw Directed Graph.  (b) To find R2=RoR.

Q: Let A = {4, 5, 6} and B = {6, 7, 8} and let S be the "divides" relation from A to B. That is, for…

A: Here given sets A = {4, 5, 6} and B = {6, 7, 8} and relation defined asxSy⇒x/y means x, y∈S⇒x…

Q: Given the relation R = {(1,2), (1,3), (2,4), (3,1), (4,2), (5,4)} on the set S = {1,2,3,4,5}. a)…

A: Given R=1,2,1,3,2,4,3,1,4,2,5,4.

Q: List the ordered pairs in the relation R from A = 0, 1, 2,3,4, B = 1,2,3, 4, 5, where R is defined…

A: Relation : A relation from a set A to a set B is a subset of A×B. i.e. a relation R consists of…

Q: Let A = { 2, 3, 4, 6 } and B = { 6, 8, 10 } and define a relation R from A to B as follows: For all…

A: Given that : A = {2, 3, 4,6} and B = {6,8,10} define relation  A*B→R R = {(x ,y): yx is an integer ,…

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: Consider the relation on A = {a, b, c, d, e} given by R ={(a,b),(b,c),(b,d),(b,e),(d,e)} .Explain…

A: Given that, A=a,b,c,d,e And R=(a,b),(b,c),(b,d),(b,e),(d,e) The graph for the diagram is,

Q: Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)}…

A: we have given relations R and S on {a, b, c, d} and we need to find composition R∘S

Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: 1. For the following, each relation R is defined on the set A. Determine if R is a tree, if it is,…

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Q: The arrow diagram below represents a relation. 1 2 3 Figure 1: An arrow diagram shous three…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 9.1. For the sets A = {a,b, c} and B= {r, s,t,w}, let R = {(a, s), (a, t) , (b,t)} be a relation…

A: Given A= {a,b,c} B={ r,s,t,u} R= { (a,s) , (a,t) , (b,t)}. We are asked to find the Domain and…

Q: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

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Q: Suppose A,S CU, (<) e LOrd(A), and B (a1,b1), (a2, b2) E (A × B): (S). If we define a relation (3)…

A: Suppose x=a,b∈A×B is an upper bound of the two point set. We have show that…

Q: A relation that assigns to each element x from a set of inputs, or ________, exactly one element y…

A: To fill: The blanks of statement: Given: The statement is "A relation that assigns to each element x…

Q: Suppose A is a set with n elements and B is a set with m elements. (a) How many ordered pairs (a, b)…

A: By bartelby guidelines I can only answer the first three sub questions.

Q: Suppose A,S C U, (<) E LOrd(A), and B := (a1, b1), (a2, b2) E (A × B): D(S). If we define a relation…

A: Given A,S⊂A ≤ is the lattice of A. B is the power set of δ , P(S) so if b1,b2 be two subsets of B.…

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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Q: Consider the following relation on set B = {1, b, {1}, {b}, {1, b}}: P = {(1, b), (b, {1, b)), ({1,…

A: Law of Trichotomy: On a set X, a binary relation R, satisfies exactly one of xRy, yRx or x=y. Where…

Q: Let X = {0, 1, 2, 3, 4}. Draw a relation R on X such that xRy if x + y = 4. a. Draw the graph…

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Q: 2. Draw a Hasse diagram for the POSET(S,R) where S = {1,2,6,8,12,18,48,72,108,144,216,432} and R be…

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Q: = {4, 5, 6} and B = {6, 7, 8}, and let S be the "divides" relation from A to B. That is, for every…

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Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…

A: Given R be the relation on the set S=1,2,3,a,b,c given by…

Q: For the following directed graph, do the following: 1. give (in set notation, e.g. { (a,b), (c,x),…

A: Given is a directed graph   1. To Find: Relation expressing the directed graph.   2. To Find:…

Q: For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2),…

A: For each of these relations on the set {1,2,3,4}, to draw the graph of the relation.

Q: Assume a directed acyclic graph is encoded as a relation R. Give a concise proposition stating that…

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Q: d b

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Q: Draw the Hasse diagram for the relation C on the set P({1,2,3}).

A: According to the given information, it is required to draw the hasse diagram for the given relation.

Q: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

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Q: et A={1,2} and B={1,2,3} and define a relation R from A to B as follows: •Given any (x,y) element A…

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Q: 1. List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,…

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

Q: For each of the following relation on the set {0,1,2,3} draw directed graphs for each relation and…

A: Consider the given set as A=0,1,2,3. (a) R1=(0,0), (0,2), (1,0), (1,3), (2,2), (3,0), (3,1) Directed…

Q: given the relation R define = (0,0), (0, 1), (0, 3), (1, 1), (1,0), (2, 3), (3, 3) on the set A = 0,…

A: Given that  R=0,0,0,1,0.3,1,1,1,0,2,3,3,3A=0,1,2,3 To draw the directed graph and determine whether…

Q: 3. Find all ordered pairs in the relation R from A = (a,b) E R if and only if a + b = 9. {0,2,4,7}…

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Q: This question refers to unions and intersections of relations. Since relations are subsets of…

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Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

Q: 1. Let A = {a, b, c} and B = {r,s, t, u}. Furthermore, let R = {(a, s), (a, t)}, (b, t) be a…

A: Suppose A and B are non empty sets. Define a relation R:A-&gt;B then, Domain of R={x: (x,y) belongs…

Q: Let A = {cat, dog, bird, rat} and R be a relation on A defined by {(r, y) : x and y have at least…

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Q: This question refers to unions and intersections of relations. Since relations are subsets of…

A: A={-4,4,7,9}B={4,7} A×B=-4,4,-4,7,4,4,4,7,7,4,7,7,7,4,7,7,9,4,9,7

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

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Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4

Q: I. Draw the directed graph and list the set of ordered pair of R, of the following. 1. If…

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