Binary Relations (antisymmetry)
A binary relation R on S is antisymmetric provided that any time we have, for some x and y, (x,y) ? R and (y,x) ? R, then x = y.
For example, the relation ? on the set of real numbers is antisymmetric, because any time we have x ? y and y ? x, it must be true that x = y.
R11 = { (a, b), (a, c), (c, c) } is antisymmetric, since the only way we could have x ? y and y ? x would be if x and y were both equal to c.
{ } is antisymmetric, since there are no violations of the antisymmetry condition.