Find the range of the realtion,`R={(x,1/x):x in Z ,0 lt x lt 6}`

Answer

To find the range of the relation \( R = \{(x, \frac{1}{x}) : x \in \mathbb{Z}, 0 < x < 6\} \), we will follow these steps:

### Step 1: Identify the domain
The domain of \( x \) is given as the integers between 0 and 6. Since \( x \) cannot be 0, the possible integer values for \( x \) are:
- \( x = 1 \)
- \( x = 2 \)
- \( x = 3 \)
- \( x = 4 \)
- \( x = 5 \)

### Step 2: Calculate the corresponding \( \frac{1}{x} \) values
Now, we will calculate \( \frac{1}{x} \) for each integer value of \( x \) identified in the previous step:
- For \( x = 1 \): \( \frac{1}{1} = 1 \)
- For \( x = 2 \): \( \frac{1}{2} = 0.5 \)
- For \( x = 3 \): \( \frac{1}{3} \approx 0.333 \)
- For \( x = 4 \): \( \frac{1}{4} = 0.25 \)
- For \( x = 5 \): \( \frac{1}{5} = 0.2 \)

### Step 3: Compile the range
The range of the relation \( R \) consists of the second coordinates from the pairs we calculated:
- The range is \( \{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}\} \).

### Final Answer
Thus, the range of the relation \( R \) is:
\[ \{1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}\} \]

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