The less-than relation on [4] is the set

R={(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}

In other words, (a,b) $\displaystyle \in$ R if and only if a < b. It contains six ordered pairs.

How many ordered pairs are in the less-than relation on [n]?

How many are in the less-than-or-equal-to relation on [n]?

The answer to the first question is $\displaystyle \sum_{i=1}^{n-1}i$ or $\displaystyle \left({n\atop 2}\right)$.

I come up with the following for the second quesiton $\displaystyle \sum_{i=1}^{n}i$ or $\displaystyle \left({{n+1}\atop 2}\right)$. Correct?