determine whether it is reflexive

For each of the following relations, determine whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive….

For each of the following relations, determine whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, or transitive. Briefly explain your answers for each one.

(a) (2 points) The domain is all CPUs. For any CPUs x and y, xRy if x has at least as many cores as y.

(b) (2 points) The domain is all people. For any people x and y, xRy if x and y are friends. Assume that everyone is his/her own friend, and that if A considers B a friend then B feels the same way about A. (This might not be true in real life, but this isn’t a social science class 🙂

(c) (2 points) The domain is all real numbers. For any real numbers x and y, xRy if |x–y| ≥ 2.

(d) (2 points) The domain is all real numbers. For any real numbers x and y, xRy if x+y = 0.