Yes, that is correct.
The less-than relation on  is the set
In other words, (a,b) 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 or .
I come up with the following for the second quesiton or . Correct?