MHT CET · Maths · Mathematical Reasoning
The negation of the statement 'He is poor but happy' is
- A He is poor but not happy.
- B He is not poor or not happy.
- C He is not poor and not happy.
- D He is neither poor nor happy.
Answer & Solution
Correct Answer
(B) He is not poor or not happy.
Step-by-step Solution
Detailed explanation
(D)
Let \(\mathrm{p}\) : He is poor and \(\mathrm{q}\) : He is happy.
The logical form of given statement is \(\mathrm{p} \wedge \mathrm{q}\).
\(\therefore \sim(p \wedge q) \equiv \sim p \vee \sim q\) i.e. He not poor or he is not happy.
Let \(\mathrm{p}\) : He is poor and \(\mathrm{q}\) : He is happy.
The logical form of given statement is \(\mathrm{p} \wedge \mathrm{q}\).
\(\therefore \sim(p \wedge q) \equiv \sim p \vee \sim q\) i.e. He not poor or he is not happy.
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