I just want to confirm my answers for prolog problems.
i)Every animal is mortal
∀X. (Animal(X)→ Mortal(X))
ii)If nobody is both a child and a dog then if Fido is a dog then Fido cannot be a child.
¬∃X. ((Child(X)^ Dog(X))→ (Dog(Fido)→ ¬Child(Fido)))
Let friend(X,Y) denote 'x is a friend of y', man(x) 'x is a man' and woman(y) 'y is a woman'. Translate into english
iii)∀X. (friend(X,Y))
Every man has at least one friend that is a woman.
iv)∃X.(man(X)^∀Y(friend(X,Y)→woman(Y)))
At least one man is a friend with all the women(in the world).
p.s Not sure if in the world should be there or if this is a closed-ended assumption. The question doesn't state that but I'm assuming the ∀ stands for all the women that exist in the entire universe.
Thank you for taking the time to look over my answers.