Quantifier Logic Some Statement – UGC NET Question

The statement “Some students are diligent” is an existential claim asserting that at least one member of the class of students has the property of being diligent. Its contradictory is “No student is diligent.” Therefore, if “some students are diligent” is true, then the statement “no student is diligent” must be false. Saying “It is not the case that no student is diligent” is logically equivalent to affirming that at least one diligent student exists.

Option A:
Option A is stronger than “some”; it claims that all students are diligent, which need not follow from the existence of at least one diligent student.

Option B:
Option B is the direct negation of the original statement and cannot be true if “some students are diligent” is true.

Option C:
Option C correctly denies the universal negative and is consistent with the existential affirmation about diligent students.

Option D:
Option D narrows the claim to exactly one student, which again is stronger than “some” and does not logically follow.