Question

1. 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?

Answer 1

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.