## Cardinalities of sets

Hi everybody, can someone please help with this?

By a graph we shall here understand the graph of a function in $[0,1]^{[0,1]}$. The paving in [0, 1] × [0, 1] = $[0,1]^2$of all graphs is denoted G. By a full set we shall here understand a subset A $\in$ [0, 1] × [0, 1] with full projection on the first axes in the sense that for every x $\in$[0, 1] there exists y $\in$[0, 1] such that (x, y) $\in$A. The paving in [0, 1] × [0, 1] of all full sets is denoted F.

Determine the cardinalities of the sets G and F. Show that no set in G can intersect every set in F.

I think that the answer to that about G is either $\aleph_0$ or $2^{2^{\aleph_0}}$, the last one being the cardinality of all real valued functions on real numbers:
Introduction to Set Theory - Google Bogsøgning
page 101