Draw the directed graph that represents the relation
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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forwardLet A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using matrixarrow_forwardDraw a directed graph for the relation R on the set {0, 1, 2, 3} given by 10. R = {(0, 1), (0, 2), (1, 2), (2, 2), (3, 1), (3, 3)}.arrow_forward
- Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric, antisymmetric, or transitive.arrow_forwardFind the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A={1,2,3}. Select one: O a. ={(2,2),(3,1),(2.2).(2,3).(3,3)}. O b. ={(1,1),(3,1),(2.2),(2,3),(3,3)}. O c. =((1,3),(3,1).(2,2), (2,3),(3,3)}. O d. ={(1,2),(1,3).(2,2),(2,3),(3,3)}. O e. ={(1,2),(3,1),(2,2),(2,3),(3,3)}.arrow_forwardQ3: Let A = {a, b, c, d} and define relations R1. R2, R3, and Ri on A, what would be their directed graph and their relationship. R= {(a, a), (c, c). (b, b), (d, d)} R= {(a, a), (a, d). (b, b), (c, c), (d, c)} R= {(a, a), (a, b). (b, a), (b, b), (c, c), (d, d)} R= {(a, c), (b, b), (b, d), (c, a), (d, d)}arrow_forward
- Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b), (a,c), (b,a), (b,c), (c,a), (c,b), (d,d), (f,f)}.arrow_forwardLet A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P),(R, P), (S, Q), (S, R)}. Find B^2 (pairs of towns that are connected by two streets). Find B^3(pairs of towns that are connected by three streets). You must use directed graph to findthe answer.arrow_forward(b) Let A = {1,2,3}. Consider the relation R on A given by R = {(1,2), (1,3), (2,1), (2,3), (3,2)} Draw the directed graph representing R. Is R transitive? Justify your answer.arrow_forward
- Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)} .Explain why R fails to be a %3D (rooted, directed) tree.arrow_forwardList all the ordered pairs in the relation R = {(a, b)| gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.arrow_forwardIf R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive and symmetric closures of the relation.arrow_forward
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