Let n be a positive integer, and let a,b,a,b Z be integers such that a a ( mod n) andb b ( mod n). Show that

(a) a a (mod n).

(b) a+ba+b(mod n).

(c) ab ab (mod n).

Let n be a positive integer, and let a,b,a',b' E Z be integers such that a E a' (mod n) and b 2 b' (mod n) . Show that (a) a E a' (mod n) . (b) a+b a'+b' (modn). (c) a b a' 52' (mod n) . Ill