Let domain of m includes all students, P (m) be the statement

let-domain-of-m-includes-all-students-p-m-be-the-statement

Let domain of m includes all students, P (m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English.

A. A student is there who spends more than 2 hours in playing polo

B. There is a student who does not spend more than 2 hours in playing polo

C. All students spends more than 2 hours in playing polo

D. No student spends more than 2 hours in playing polo

I had been asked this question in homework.

My doubt stems from Predicate Logic Quantifiers in portion The Foundation: Logics and Proofs of Discrete Mathematics

Right answer is D. No student spends more than 2 hours in playing polo

Explanation: There is no student who spends more than 2 hours in playing polo.