Given two sets:
A={ Me, Ve, Ea, Ma, Jup, Sat, Ura, Nep} ;
B={Eu, Io, Dei, Fo}.
I need to express the following statements in terms of predicates and quantifiers:
(a) There is a planet that does not orbit the sun;
(b) All planets and their moons orbit the sun;
(C) Not all moons that orbit the sun orbit Mars.
In my textbook there is no similar problem so I don't know how to solve it.
I was thinking that if P(x)is the statement "x orbits the sun", then (a) becomes
$\exist x\in A(\neg P(x))$.
For (b) I think it is
$\forall x\in A\cup B P(x)$.
Then if Q(x,y) is x orbits y for (c) we have
$(\neg \forall x\in B)( Q(x, Sun))(Q(x, Mars)).$
Am i right??