Solution for Section 10.2 Question 2

2.  i) For all positive integers a, a | a, since a = a � 1, so the "divides" relation is reflexive.

ii) For all positive integers a and b, if a | b, then b = a � k for some integer k. However, this does not imply that b | a, (for instance, let a = 2 and b = 4), so the "divides" relation is not symmetric.

iii) For all positive integers a, b and c, if a | b and b | c, then b = a � p for some integer p and  c = b � q for some integer q. Hence c = (a � p) � q = a � r for some integer r, and so a | c. Therefore, the "divides" relation is transitive.

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