Abstract math, sets and logic proof

[beatka6]

Homework Statement

If A is a set that contains a finite number of elements, we say A is a finite set. If
A is a finite set, we write |A| to denote the number of elements in the set A. We
also write |B| < ∞ to indicate that B is a finite set. Denote the sets X and Y by
X = {T : T is a proper subset of P(Z) or |T| < ∞}; Y = {T element of X : T≠ ∅}
Prove or disprove the following:
(there exist X element of R)(∅ element of R and ( for all S element of Y)(|R|≤ |S|}

Homework Equations

The Attempt at a Solution

I think that statement is true because of or in the statement, but I have no idea how to prove it

 

[kru_]

I can't understand what it is that you are trying to show. Can you write it out in words?

 

[beatka6]

It s number 5 from the attachment.