Let S a b c Recall that a relation on S is a subset of SS G

Let S = {a, b, c}. Recall that a relation on S is a subset of S×S. Give
an example of a relation R on S that is reflexive and:
a. Symmetric but not anti-symmetric.
b. Anti-symmetric but not symmetric.
c. Neither symmetric nor anti-symmetric.
b. Both symmetric and anti-symmetric.

Solution

a) ((a,a),(b,b),(c,c),(a,b),(b,a),(a,c),(c,a),(b,c),(c,b) )

b) ((a,a),(b,b),(c,c),(a,b),(c,a),(b,c))

c)((a,a),(b,b),(c,c),(a,b),(c,a))

d)((a,a),(b,b),(c,c))