Write the relation `R={(x, x^{2}).`, where `x` is an odd.natural number less than 7`}`. Find the number of relation.

Options

A. 2
B. 3
C. 4
D. 5

Answer

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

### Step 1: Identify the odd natural numbers less than 7
Odd natural numbers are those that are not divisible by 2. The odd natural numbers less than 7 are:
- 1
- 3
- 5

### Step 2: Write the relation R
The relation R is defined as R = {(x, x²) | x is an odd natural number less than 7}. We will find the pairs by substituting the identified odd natural numbers into the relation.

### Step 3: Calculate x² for each odd natural number
Now we will calculate x² for each of the identified odd natural numbers:
- For x = 1:
- (1, 1²) = (1, 1)
- For x = 3:
- (3, 3²) = (3, 9)
- For x = 5:
- (5, 5²) = (5, 25)

### Step 4: List all pairs in the relation R
Based on the calculations, the relation R can be written as:
R = {(1, 1), (3, 9), (5, 25)}

### Step 5: Count the number of pairs in the relation R
Now, we count the number of pairs in the relation R. We have:
- (1, 1)
- (3, 9)
- (5, 25)

Thus, there are a total of 3 pairs.

### Final Answer
The number of relations R is **3**.

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