Let R be a relation on the set A = {0, 1, 2, 3} defined as follows: R = {(0, 1), (1, 2), (1, 1), (2, 1), (0, 2), (2, 0)} Draw the directed graph of R. ( attach the pdf file with the directed graph)
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- 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)= {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} Draw the directed graph of the relation R X= {1,2,3,4}.Draw 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)}.
- Let A={1,2,3,4} and let R be the relation from A to A R={(1,1),(1,4),(2,1),(2,2),(2,3),(3,1),(3,4),(4,3)} Create thr diagraph and matrix Mr for the relation(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.Find 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)}.
- The relation R on set A = {0, 1, 2, 3, 4, 5} is given by R = {(0, 0), (0, 1), (0, 5)(1,0),(1, 1), (1, 5), (2, 2), (2, 4), (3, 3), (4, 2), (4, 4), (5, 0), (5, 1), (5, 5)}. (i) Determine whether the relation R is reflexive, irreflexive, symmetric,antisymmetric, asymmetric, or transitive. Give a counterexample or anexplanation if your answer is “No”.Let 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.Let B = {1, 2, 3, 4} and S be the relation defined by S = {(1,1), (1,3), (1,4), (2,2), (2,4), (3,3), (3,4), (4,4)}. Determine the relation S is a partial ordered relation.
- Let R be a relation on the set {a,b, c, d} R = {(a, b), (a, c), (b, a), (d, b)} Find: 1) The reflexive closure of R 2) The symmetric closure of R 3) The transitive closure of R Express each answer as a matrix, directed graph, or using the roster method (as above). Don't express your answer in terms of set operations.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)}.Define a relation R, on the set A = {0, 1, 2, 3} as follows. R, = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3) (a) Which of the following is the directed graph of R,? (b) Is R, reflexive, symmetric, transitive, or none of these? (Select all that apply.) O R, is reflexive. O R, is symmetric. O R, is transitive. O R, is neither reflexive, symmetric, nor transitive.