When `A= phi` then number of elements in P(A) is

Options

A. 1
B. 2
C. 0
D. 3

Answer

To solve the question, "When A = φ (the null set), then the number of elements in P(A) is:", we will follow these steps:

### Step 1: Understand the definition of a null set
A null set, denoted as φ, is a set that contains no elements.

**Hint:** Remember that the null set is defined as having zero elements.

### Step 2: Define the power set
The power set P(A) of a set A is the set of all possible subsets of A.

**Hint:** The power set includes the empty set and the set itself.

### Step 3: Calculate the number of elements in the power set
The formula for the number of elements in the power set of a set A is given by:
\[ N(P(A)) = 2^{N(A)} \]
where \( N(A) \) is the number of elements in set A.

**Hint:** You need to know how to apply the formula for the power set.

### Step 4: Apply the formula to the null set
Since A = φ, we have:
\[ N(A) = 0 \]
Now, substituting this into the formula:
\[ N(P(A)) = 2^{N(A)} = 2^0 \]

**Hint:** Remember that any number raised to the power of zero equals one.

### Step 5: Calculate the result
Now, calculating \( 2^0 \):
\[ 2^0 = 1 \]

**Hint:** This is a fundamental property of exponents.

### Conclusion
Thus, the number of elements in the power set P(A) when A = φ is 1.

**Final Answer:** The number of elements in P(A) is 1.