If P={x:x is a prime number is less than 20} and M={x:x is a multiple of 6, `0 lt x lt 30}` then n(P)-n(M) is

Options

A. 2
B. 4
C. 5
D. 8

Answer

To solve the problem, we need to determine the number of elements in the sets \( P \) and \( M \), and then find the difference \( n(P) - n(M) \).

### Step-by-Step Solution:

1. **Define the Set \( P \)**:
- The set \( P \) is defined as \( P = \{ x : x \text{ is a prime number and } x < 20 \} \).
- Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.

2. **List the Prime Numbers Less Than 20**:
- The prime numbers less than 20 are:
- 2, 3, 5, 7, 11, 13, 17, 19.
- Therefore, the set \( P \) can be written as:
\[ P = \{ 2, 3, 5, 7, 11, 13, 17, 19 \} \]

3. **Count the Elements in Set \( P \)**:
- The number of elements in set \( P \) is:
\[ n(P) = 8 \]

4. **Define the Set \( M \)**:
- The set \( M \) is defined as \( M = \{ x : x \text{ is a multiple of 6 and } 0 < x < 30 \} \).

5. **List the Multiples of 6 Between 0 and 30**:
- The multiples of 6 less than 30 are:
- 6, 12, 18, 24.
- Therefore, the set \( M \) can be written as:
\[ M = \{ 6, 12, 18, 24 \} \]

6. **Count the Elements in Set \( M \)**:
- The number of elements in set \( M \) is:
\[ n(M) = 4 \]

7. **Calculate \( n(P) - n(M) \)**:
- Now, we need to find the difference:
\[ n(P) - n(M) = 8 - 4 = 4 \]

### Final Answer:
The value of \( n(P) - n(M) \) is \( 4 \).

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