If A is the set of even natural numbers less than 8 and B in the set prime numbers less than 7, then the number of relations from A to B is

Options

A. `2^(9)`
B. `9^(2)`
C. `3^(2)`
D. `2^(9)-1`

Answer

To solve the problem, we need to follow these steps:

### Step 1: Identify the sets A and B.
- **Set A**: The set of even natural numbers less than 8.
- The even natural numbers less than 8 are: 2, 4, and 6.
- Therefore, \( A = \{2, 4, 6\} \).

- **Set B**: The set of prime numbers less than 7.
- The prime numbers less than 7 are: 2, 3, and 5.
- Therefore, \( B = \{2, 3, 5\} \).

### Step 2: Determine the number of elements in sets A and B.
- The number of elements in set A, denoted as \( m \):
- \( m = |A| = 3 \) (since there are three elements: 2, 4, and 6).

- The number of elements in set B, denoted as \( n \):
- \( n = |B| = 3 \) (since there are three elements: 2, 3, and 5).

### Step 3: Use the formula for the number of relations from set A to set B.
- The number of relations from set A to set B is given by the formula:
\[ \text{Number of relations} = 2^{m \times n} \]
- Substituting the values of \( m \) and \( n \):
\[ \text{Number of relations} = 2^{3 \times 3} = 2^9 \]

### Step 4: Calculate \( 2^9 \).
- \( 2^9 = 512 \).

### Final Answer:
The number of relations from set A to set B is **512**.

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