What is the logical translation for the following statement?
\”Not all boys are Intelligent\”

(A) ∀x(Boy(x)) → Intelligent(x))
(B) ∀x(¬Boy(x)) ∧ Intelligent(x))
(C) ∃x(Boy(x)) → ¬Intelligent(x))
(D) ∃x(Boy(x)) ∧ ¬Intelligent(x))


Answer: (D)

Explanation: First, consider the statement as “All boys are Intelligent”
We can write it as ∀x(Boy(x)) → Intelligent(x))

Then negate it.

¬[∀x(¬Boy(x)) → Intelligent(x))]
∃x(Boy(x)) ∧ ¬Intelligent(x))

Quiz of this Question