$∀m, ∀n, ∃l | (n<m) ⇒ (l>n)∧(l<m)$

Question

I have to show if the following proposition is true or false and prove my answer. $l,m,n$ ∈ {whole numbers} = {$0,1,2,3...$}.

I'm thinking to do a contrapositive on each side. So by putting the left side $(∀ m, ∀ n, ∃ l | (n < m)) = P$ and right side $((l > n)∧(l < m))$ = Q to show if P⇒Q = ¬Q⇒¬P and if $¬Q⇒¬P$ is true then $P⇒Q$ is also true.

I'm new to Discrete Math; sorry for my lack of knowledge. Thanks for your help.

Answer 1

This is not true, for if $m,n$ are consecutive numbers there does not exist some $l$ between $m$ and $n$ which is not equal to $m$ or $n$.