The negation of "Some students like hockey" is:
2022
The negation of "Some students like hockey" is:
- A.
Some students dislike hockey
- B.
Every student dislike hockey
- C.
Every student like hockey
- D.
All students like hockey
Attempted by 156 students.
Show answer & explanation
Correct answer: B
Negation concept: The statement "Some students like hockey" means "There exists at least one student who likes hockey."
Formal negation: The negation of "there exists at least one student who likes hockey" is "there does not exist a student who likes hockey."
Equivalent phrasing: "There does not exist a student who likes hockey" is equivalent to "No students like hockey" or "Every student does not like hockey."
Why other choices are wrong: Saying "Some students dislike hockey" does not contradict the original statement because both could be true at once.
Why other choices are wrong: Saying "Every student likes hockey" or "All students like hockey" asserts a universal positive (everyone likes hockey), which is not the logical negation of "some like hockey."
Conclusion: The correct negation is that no students like hockey (equivalently, every student does not like hockey).
A video solution is available for this question — log in and enroll to watch it.