I've been asked to write down a statement using predicate calculus and it is confusing me a great deal.
I've got statement A "no dog can fly" and B "There is a dog which can fly" D = set of all dogs , F = set of all creatures that can fly P(x) is the proposition that "creature x can fly" Q(x) is the proposition that "creature x is a dog"
How do I write statements A and B using predicate calculus in terms of P(x)?
I wrote for A: ∀x(P(x)→¬Q(x) and B: ∃x(P(x)→Q(x) but this doesn't seem right to me at all. Anyone got a suggestion?
The statement A is OK, apart from a missing parenthesis. Statement B should be something like $\exists x(Q(x)\land P(x))$.
Your version of B would be true if there were, for example, no flying creatures.
There are always many equivalent ways of stating things. Closer in tone to the English statement of A is $\forall x(Q(x)\longrightarrow \lnot P(x))$. Or maybe $\lnot\exists x(Q(x)\land P(x))$.