The negation of "Some students like hockey" is:

2022

The negation of "Some students like hockey" is:

  1. A.

    Some students dislike hockey

  2. B.

    Every student dislike hockey

  3. C.

    Every student like hockey

  4. D.

    All students like hockey

Attempted by 156 students.

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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).

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