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?

It isn't reflexive. (Why? Try letting $k=i$ and $l=j$ and see if things still work.)
To see why it's symmetric, notice that we can obtain $k<i\wedge i\le l\le j$ from $i<k\wedge k\le j\le l$ (and vice versa) by simply swapping $i$ with $k$, and $j$ with $l$.
Since it's symmetric, but not reflexive, then it can't be transitive. (Why?)
