Let S = {1,2....10} Let R be the relation on P(S), the power set of S, defined by: for any X,Y ∈ P(S),

Question

Let S = {1,2....10} Let R be the relation on P(S), the power set of S, defined by: for any X,Y ∈ P(S),

XRY <=> X∩Y=∅

is it true that ∀X∈P(S),∃Y∈P(S) so that (X,Y)∈R?

I dont know what is (X,Y)?

how many sets X∈P(S) are there so that XR{10}? help me on this one please

Answer 1

Hint: $X$ has some elements. What happens if $Y$ has any of them?

Answer 2

Remember the power set of $S$ is the set of all possible subsets of $S$. So if $X\in P(S)$, what set is also in $P(S)$ that has no elements of $X$?