Proof of cardinality inequality: $m_1\le m_2$, $k_1\le k_2$ implies $k_1m_1\le k_2m_2$ I have this homework question I am struggling with:
Let k1,k2,m1,m2 be cardinalities. prove that if $${{m}_{1}}\le {{m}_{2}},{{k}_{1}}\le {{k}_{2}}$$ then $${{k}_{1}}{{m}_{1}}\le {{k}_{2}}{{m}_{2}}$$ 
Can anyone please help me prove this?
thanks

Do it in three steps, each of which should be straightforward:
(i) $k_1m_1 \le k_2m_1$;
(ii) $k_2m_1 \le k_2m_2$;
(iii) Therefore by transitivity $k_1m_1 \le k_2m_2$.
Given the way homework questions are usually designed, each step is likely to be justifiable by quoting appropriate results given in the course.  If not, justification is still not difficult.  
