Question

Domain is all creatures, and predicates defined as follows:

C(x) = “x is a cat.”    D(x) = “x is a dog.”    S(x) = “x is a celebrity.”

L(x,y) = “x likes y.”

Translate into predicate logic (use quantifiers ∃,∀ where necessary):

1. "No dog likes a celebrity"

I think the answer is ∀ x∃y[D(x) → S(y) ∧ L'(x,y)] but I'm not sure if I'm correct and would like to check with someone else.

Answer 1

From the question:

C(x) = “x is a cat.”

D(x) = “x is a dog.”

S(x) = “x is a celebrity.”

L(x,y) = “x likes y.”

1. "No dog likes a celebrity"

No dog likes, it means that all dogs does not like all of the celebrities.

Thefore use ∀x and ∀y

∀ x ∀ y((D(x)/\S(y)) → ¬L(x, y)