Set Theory

Let S = {1, 2, 3, 4, 5, 6} and X be the set of all relations R from S to S that satisfy both the following properties :
i. R has exactly 6 elements.
ii. For each (a, b) ∈ R, we have |a - b| ≥ 2.
Let Y = {R ∈ X : The range of R has exactly one element} and
Z = {R ∈ X : R is a function from S to S}.
Let n(A) denote the number of elements in a set A.