Is the relation reflexive, anti-reflexive, or neither? Is

Is the relation reflexive, anti-reflexive, or neither?

Is the relation symmetric, anti-symmetric, or neither?

Is the relation transitive?

If the relation does not have one of the properties, give a counterexample. (Normally this will be an ordered pair that is in the relation when the property forbids it, or isn’t in the relation when the property requires it.)

a) The domain is a set of people; (x, y) is in the relation if person x is taller than person y. 

b) The domain is the set of real numbers; (x, y) is in the relation if x – y is a rational number.

c) The domain is A = {a, b, c, d}; the relation is {(a,b), (a, a), (b, b), (b, a), (c, d), (d, c)}.