1. Let R be the relation on A = {1, 2, 3, 4, 5} given by...

1. Let R be the relation on A = {1, 2, 3, 4, 5} given by R = {(1, 1),(1, 3),(2, 2),(2, 4),(2, 5),(3, 1),(3, 3),(4, 2),(4, 4),(4, 5),(5, 2),(5, 4),(5, 5)}.

(a) Draw the digraph which represents R.

(b) Give the 0 -1 matrix of R with respect to the natural ordering.

(c) Which of the five properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does R have? Give a brief reason why or why not each property holds.

2. Let A = {1, 2, 3, 4}, B = {α, β, γ}, and C = {x, y, z}. Further suppose S = {(1, γ),(2, α),(2, γ),(3, β),(3, γ)} and R = {(α, x),(α, y),(β, z)}.

(a) Compute the composition relation R ◦ S. Hint: It may be helpful to draw bipartite graphs.

(b) Is the relation R ◦ S a function from A to B? Why or why not?

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Expert Solution

Colby Messinger answered 1 week ago

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