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math_proof
 3 years ago
(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.
math_proof
 3 years ago
(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.

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