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

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Q: 2. Let A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and suppose R is a relation defined by a is related to b…

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

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,…

Q: Consider the set A ={(1, 3), (2, 4), (-4,-8), (3, 9), (1, 5), (3, 6). Define the relation R on A as…

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Q: 11. Let A(3, 4, 5) and B=(4,5,6) and let S be the "divides" relation. That is, for all (x, y) e Ax…

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Q: let A= {a, b, c, d} and R= { (a,a), (a, c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. draw a…

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Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

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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: Consider following five sets: I.{ , } { } II. { } III. IV. { , , } V. { , } Find all set(s)…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let A be the set A = {a, b, c, d} and R a relation on A defined as the following:   R = {(a, a), (a,…

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Q: 1. Suppose A = {1,2, 3, 4} and the relation R on A is R = {(1,1), (2, 2), (3,3), (3, 4), (4, 4)} (a)…

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Q: 8. Let A = {2, 4} and B = {1, 3, 5} and define relations U, V, and W from A to B as follows: For all…

A: In the given question we have to draw the arrow diagram of the relation U,V and W and we have to…

Q: 5. Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For…

A: Given: A={6, 8, 10, 15, 17} B={2, 3, 4, 5} Relation R:A→B is: For all x,y∈A×B∈R if and only if…

Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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Q: Suppose A and B are two finite sets such that |B| = 2 |A| and the number of relations on A is 16.…

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Q: 1. Let A = {2, 3, 4, 5, 6} and B = {10, 11, 12, 13). Define a relation R on (A x B) as follows: a Rb…

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