Let R be a relation on a function F from A to A.

Now, 

1. R is reflexive iff for all x ∈ A, xRx

2. R is symmetric iff for all x, y ∈ A, if xRy then yRx

3. R is transitive iff for all x, y, z ∈ A, if xRy and yRz then xRz

Ex:  Let A = { 0,1,2,3} and a relation R on A be given by

R = {(0,0), (0,1), (0,3), (1,0), (1,1), (2,2), (3,0), (3,3)}

Is R reflexive? symmetric? transitive?

Solution:

a) R is reflexive. This is because (0, 0), (1, 1), (2, 2), (3, 3) exists.

(b) R is symmetric. This is because for (0, 1), (1, 0) exists and (0, 3), (3, 0) exists.

(c) R is not transitive. This is because for (1, 0) and (0, 3), (1, 3) does not exists.