Question

Negation of the statement 'It is night or all stars are shining' is

• A. It is not night and all stars are not shining
• B. It is night and all stars are not shining
• C. It is not night or all stars are not shining
• D. It is night or all stars are not shining

Answer 1

Answer: (A)

It is not night and all stars are not shining

Answer 2

Let

$P: \text{"It is night"}$

$Q: \text{"All stars are shining"}$

The given statement is

$P \lor Q.$

Using De Morgan’s Law, the negation is:

$\neg (P \lor Q) \equiv \neg P \land \neg Q.$

This translates to:

• It is not night, and

• It is not true that all stars are shining (i.e., at least one star is not shining).

Apply De Morgan’s law:

$\neg (P \lor Q) = \neg P \land \neg Q$.