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Question
Write the negation of the following statement.
All the stars are shining if it is night.
Solution
Let q : All stars are shining.
p : It is night.
The given statement in symbolic form is p → q.
It’s negation is ~ (p → q) ≡ p ∧ ~ q
∴ The negation of a given statement is 'It is night and some stars are not shining'.
Notes
The answer in the textbook is incorrect.
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