Q: Which of the following statements about negating quantified statements are correct?
(A) The negation of “all swans are white” is “no swans are white”;
(B) The negation of “all swans are white” is “some swans are not white”;
(C) The negation of “no students are late” is “some students are late”;
(D) The negation of “some teachers are not researchers” is “all teachers are not researchers”;
(E) To negate a universal statement, we typically change “all” to “some” and introduce a negation inside the predicate;
Choose the correct answer from the options given below:
Q: Which of the following statements about quantifiers in logical reasoning are correct?
(A) The quantifier “all” usually corresponds to universal statements about every member of a class;
(B) The quantifier “some” in logic means at least one, and possibly all, members of a class;
(C) The quantifier “no” can be understood as “for all, not”, as in “for all S, S is not P”;
(D) In ordinary language, “some” always implies “not all” and never allows the possibility that all may satisfy the property;
(E) In UGC NET syllogism questions, careful reading of quantifiers prevents mistaken inferences;
Choose the correct answer from the options given below:

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