Question

Which of the following is true?

• A. Φ = 0
• B. n(Φ) = 0
• C. Φ = {0}
• D. n(Φ') = 0

Answer 1

The Correct Option is B

To solve the problem, we need to identify the correct statement related to the null set (empty set).

1. Understanding the Symbols:
- $ \phi $ denotes the null set (an empty set with no elements).
- $ n(\phi) $ denotes the number of elements in the set $ \phi $.

2. Analyzing Each Option:
(1) $ \phi = 0 $ → Incorrect, because $\phi$ is a set, not a number.
(2) $ n(\phi) = 0 $ → Correct, because the number of elements in the null set is 0.
(3) $ \phi = \{0\} $ → Incorrect, because $\phi$ is an empty set, but $\{0\}$ is a set containing one element: 0.
(4) $ n(\phi') = 0 $ → Incorrect, as $\phi'$ usually refers to the complement of $\phi$, which is not defined without a universal set.

Final Answer:
The correct statement is $ \mathbf{n(\phi) = 0} $.