Let the set A be defined as A a b c d and let the relation

Let the set A be defined as A = {a, b, c, d}, and let the relation R on the set A be defined by R = {(d, a), (a, b), (a, a), (b, c)}. Explain why R is or is not symmetric, and why R is or is not reflexive.

Solution

R is symmetric if and only if for every :(x,y) in R (y,x) must also be in R

(d,a) is in R but (a,d) is not in R. Hence R is not symmetric.

R is reflexive if and only if for every x in A ,(x,x) is in R

But, we see

(d,d),(c,c),(b,b) is not in R. Hence R is not reflexive.