Let S $=\{50,1,2,4,66\}$

Test the following binary relations on S for reflexivity, symmetry, antisymmetry, and transitivity.

Find the reflexive, symmetric, and transitive closure of each of the relations

a$.\backslash$rho $=\{(0,0),(1,1),(2,2),(4,4),(6,6),(0,1),(1,2),(2,4),(4,6)\}$

b$.\backslash$rho $=\{(0,1),(1,0),(2,4),(4,2),(4,6),(6,4)\}$

c$.\backslash$rho $=\{(0,1),(1,2),(0,2),(2,0),(2,1),(1,0),(0,0),(1,1),(2,2)\}$

d$.\backslash$rho $=\{(0,0),(1,1),(2,2),(4,4),(6,6),(4,6),(6,4)\}$

e$.\backslash$rho $=\{\}$