Prove that Big-O is transitive by relation. What does it mean by 'by relation'? Prove $f(n) = O(g(n))$ and $g(n) = O(h(n))$, then $f(n) = O(h(n))$.

The question is 


  Prove that Big-O is transitive by relation. 


What does it mean by by relation??
f(n)=O(g(n)) implies f(n) &lt;= c1*g(n)
g(n)=O(h(n)) implies g(n) &lt;= c2*h(n)
therefore, 
f(n) &lt;= c1*c2*h(n) = c3*h(n)

f(n) &lt;= c3*h(n) implies f(n)=O(h(n))