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Which of the following represents: ~A (negation of A) if A stands for “I like badminton but hate maths”?

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Which of the following represents: ~A (negation of A) if A stands for “I like badminton but hate maths”?

(a) I hate badminton and maths

(b) I do not like badminton or maths

(c) I dislike badminton but love maths

(d) I hate badminton or like maths

The question was asked in homework.

This is a very interesting question from Logics and Proofs in section The Foundation: Logics and Proofs of Discrete Mathematics

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The correct choice is (d) I hate badminton or like maths

The explanation: De Morgan’s Law ~ (A ∧ B) ↔ ~A V ~B.

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