(a) All students who like computer science like mathematics.(S(x), C(x), M(x))
(b) There are some students who like Socrates but do not like Aristotle. (S(x), L(x, y), S, A)
(c) No student who likes computer science also likes Oscar. (O, S(x), C(x), L(x, y))
We are supposed to use the predicate symbols provided. This was our first lecture on this topic so I am fairly new to predicate Calculus. For (a), I think I am correct with my result: ∀x ((S(x) ^ C(x)) -> M(x))
But for (b) and (c) I have absolutely no clue how to implement the symbols L(x, y) into the final result. Any help would be very much appreciated.
$$(a)\qquad \forall x([S(x) \land C(x)]\implies M(x))$$
$$(b)\qquad \exists x(S(x) \land L(x,S) \land \lnot L(x,A))$$
$$(c)\qquad \lnot \exists x(S(x) \land C(x) \land L(x,O))$$
or perhaps
$$(c)\qquad \forall x([S(x) \land C(x)] \implies \lnot L(x,O))$$
So your answer to (a) was correct, even if not correctly typeset.