Question

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.

Hint:

To negate statements involving "but", use De Morgan's laws: "not P or not Q" for "P but Q".

Answer 1

The Correct Option is B

Step 1: Understand the logic.
The original statement is "He is poor but happy". The negation of this statement is formed by negating the individual components using De Morgan's laws.
Step 2: Apply De Morgan's law.
The negation of "He is poor but happy" is "He is not poor or not happy," which is option (B).
Step 3: Conclusion.
Thus, the negation of the statement is "He is not poor or not happy," corresponding to option (B).