#### Answer

-D is Reflexive
-D is not symmetric
-D is transitive

#### Work Step by Step

--D is reﬂexive:
-[We must show that for all positive integers m,m D m.]Suppose m is any positive integer. Since m = m·1, by deﬁnition of divisibility m | m. Hence m D m by deﬁnition of D.
-- D is not symmetric:
- For D to be symmetric would mean that for all positive integers m and n, if m D n then n D m . By deﬁnition of divisibility, this would mean that for all positive integers m and n, if m|n then n|m. But this is false. As a counterexample, take m =2 and n =4. Then m|n because 2|4 but n (not|)m because 4(not|2).
-- D is transitive:
- To prove transitivity of D, we must show that for all positive integers m,n, and p, if m D n and n D p then m D p. By deﬁnition of D, this means that for all positive integers m,n, and p, if m|n and n | p then m | p.