Let n be a natural number. Prove each of thefollowing:

(a) For every integer a, a = a (mod n). This is called thereflexive property of congruence modulo n.

(b) For all integers a and b, if a = b (mod n), then b = a (modn). This is called the symmetric property of congruence modulon.

(c) For all integers a, b, and c, if a = b (mod n) and b = c(mod n), then a = c (mod n). This is called the transitive propertyof congruence modulo n.