Question

can any body help me plse....

Let a be an integer which is related to another integer b. if a is a multiple of b .
How can we prove or check that the relation is reflexive, symmetric and transitive

Answer 1

Let us denote a being a multiple of b as \(b|a\). Reflexivity is clearly true; every number divides itself, i.e. \(n|n\). Symmetry, however, does not hold; \(1|n\) for any integer \(n\) but \(n|1\) is not true for any integer not \(1\). Transitivity holds, however -- if \(b|a\), it followsthat \(a=k_1b\) for some integer \(k_1\) (this is what being a multiple means\); say that \(a|c\) for some \(c\), i.e. \(c=k_2a\) for some integer \(k_2\), so then \(c=k_1k_2b\) and therefore \(b|a\land a|c\implies b|c\).

Answer 2

http://en.wikipedia.org/wiki/Divisor