(1) Show that if n 0 is a positive integer then the relation ≡n on integers defined by a ≡n b if n|(a − b) is an equivalence relation.
(2) When n = 2, what are the equivalence classes? Can you see the connection with question 1?
(3) What are the equivalence classes when n = 3? (4) Foragivenn1,supposethata ≡n bandc ≡n d. Provethata+c ≡n b+dand
ac ≡n bd.

Question

(1) Show that if n > 0 is a positive integer then the relation ≡n on integers defined by a ≡n	b if n|(a − b) is an equivalence relation.
(2) When n = 2, what are the equivalence classes? Can you see the connection with question 1?
(3) What are the equivalence classes when n = 3? (4) Foragivenn>1,supposethata ≡n bandc ≡n d. Provethata+c ≡n b+dand
ac ≡n bd.