The domain of the following predicates is all integers greater than 1.

P(x) = “x is prime”

Q(x,y) = “x divides y”

Consider the following statement.

“For every x that is not prime, there is some prime y that divides it”

i. Write the statement in predicate logic.

ii. Formally negate the statement so that no quantifier lies in the scope of the

negation.

iii. Write the English translation of your negated statement

I tried this and I got

i. ∀x¬P(x)∃xQ(x,y)

ii. ∃xP(x)∀x¬Q(x,y)

iii. There exists a x that is prime, there is y for every prime that does not divide it.

Thanks