Let n be a natural number. Prove each of thefollowing: (a) For every integer a, a =
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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.
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