Let X be a set.
Then XX, since every set is a subset of itself.
Therefore, R is reflexive.
Let X and Y be sets, and suppose XY.
It is not necessarily so that XY implies YX.
Consider the counterexample X=cfw_1, 2 and Y=cfw_1, 2, 3.
Let be a real number such that " > 16.
Then " > 16, which means that 4 < < 4.
Therefore, = 5 is a counterexample to the above statement.
We will prove this statement by contradiction.
Let be rational and be ir