Proving reflexivity, symmetry and transitivity on a relation. I am trying to see if the following relation is reflective, symmetric and transitive:
$(i, j),(k, l)$ are in relation R if:
$(i < k$ $\land $ $k \le j \le l) \lor (k < i$ $\land$ $i \le l \le j )$
The only exercices I had on this subject was to prove reflexivity/symmetry/transitiviy for really simple binary relations such as:
$(x, y) R (s, t) = (x + y) = (s + t)$
For a simple case like this, I know how to proceed. The thing that confuses me is when I have to deal with couples and inequalities. I simply don't know how to approach the problem.
Anyone could point me in the right direction so I know how to deal with these couples/inequalities?

There really is nothing different about this sort of problem even if the relation involves inequalities.
Reflexive: Is is true that that for all $(i,j)$, $(i,j)R(i,j)$?
Symmetric: Is it true that if $(i,j)R(k,l)$, then $(k,l)R(i,j)$?
Transitive: Is it true that if $(i,j)R(k,l)$ and $(k,l)R(m,n)$, then $(i,j)R(m,n)$?
Write out what these statements would mean by the definition of $R$, then determine if the statement is true or false.
