How do I specify the domain of a quantifier? How do I specify the domain of a quantifier? > A = {x | x is an animal} > > ∀x(Dog(x) → Bark(x)) Is this correct? > (∀x ∈ A)(Dog(x) → Bark(x))

$$\forall x \in A (Dog(x) \implies Bark(x))$$ is actually a shorthand for $$\forall x[x \in A \implies (Dog(x) \implies Bark(x))]$$ which could be read as 'given a thing $x$, if $x$ is an animal then if it is a dog it barks', or in a shorter way 'given any animal $x$, if $x$ is a dog then $x$ barks', so yes, it is correct to specify the domain of your quantifier in that way