The negation of the statement 'He is poor but happy' is
The negation of the statement 'He is poor but happy' is
He is poor but not happy.
He is not poor or not happy.
He is not poor and not happy.
He is neither poor nor happy.
Solution
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.