Given: p | q means p divides q
q | p means q divides p
proof: Since p divides q then it can be written as q = p*k where k $\epsilon$ Z
so k = $\frac{p }{q}$ --- eq 1
and q divides p then it can be represented as p = q*m where m $\epsilon$ Z
so m = $\frac{q }{p}$ ----eq 2
from eq 1 and eq 2 it can be said that
k = $\frac{1 }{m}$
so m * k = 1
now , since m and k are integers and their product is 1
hence m = k =1
so from eq 1 we can substitute value of k which is 1
1= $\frac{p }{q}$
so , q =p [hence proved].