Answer: So the set is X > 1, X ⊂ N
so x ∈ X = {2,3,4,5.....}
So the statement is, if x.y ∈ X
then x cant divide (x*y +1)
you can see this using the distributive property in the next way:
[tex]\frac{x*y + 1}{x} = \frac{x *y}{x} + \frac{1}{x} = y + \frac{1}{x}[/tex]
where y is a natural, and 1/x is a irrational number, the addition of a natural and a irrational number is an irrational number.
then [tex]\frac{x*y + 1}{x}[/tex] is irrational, this means that x does not divide x*y +1.
