(a) Give an example of a relation R on a set A that is antisymmetric and such that x R x for some, but not all, x in A. (b) Give an example of a relation S on the set A={a,b,c,d} such that S is
a) (a,a) for R; (a,b) and (b,a) for S
b) (a,a) and (a,b) for R; (b,a) for S
c) (a,a) for R; (a,b) and (b,c) for S
d) (a,b) and (b,a) for R; (a,a) for S