Given the following relation, { ( A, A ), ( A, B ), ( A, D...

Given the following relation, { ( A, A ), ( A, B ), ( A, D ), ( B, B ), ( B, C ), ( B, E ), ( C, B ), ( C, C ), ( C, D ), ( D, A ), ( D, B ), ( D, C ), ( D, E ), ( E, D ), ( E, E ) }
i) Draw the digraph of the relation, ii) construct the matrix diagram for the relation, and iii) why or why not is the relation reflexive, symmetric, antisymmetric, transitive?

Expert Solution

i) first we mark 5 vertices A,B,C,D,E .then if (A,B) in relation R then draw an edge from A to B directed towards B.repeating this we draw digraph.

ii) if (A,A) is in the relation then matrix a₁₁ th entry is 1.

iii) diagonals of A^' not all 1.so relation is not reflexive.A' is not symmetric matrix so relation is not symmetric.

(A,D) and (D,A) is in the relation bit A not equal to B hence the given relation is not antisymmetruc.

(C,D) and (D,E) is in the relation.but (C,E) is not in the relation.so the given relation is not transitive.

Colby Messinger answered 2 years ago

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