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Question
The negation of the statement “72 is divisible by 2 and 3” is ______.
Options
72 is not divisible by 2 or 72 is not divisible by 3
72 is not divisible by 2 and 72 is not divisible by 3
72 is divisible by 2 and 72 is not divisible by 3
72 is not divisible by 2 and 72 is divisible by 3
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Solution
The negation of the statement “72 is divisible by 2 and 3” is 72 is not divisible by 2 and 72 is not divisible by 3.
Explanation:
Let p: 72 is divisible by 2 and 3
And q: 72 is divisible by 2
r: 72 is divisible by 3
∴ ~ q: 72 is not divisible by 2
~ r: 72 is not divisible by 3
So ~ (q ∧ r) : ~ q ∨ ~ r
⇒ 72 is not divisible by 2 or 72 is not divisible by 3.
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