Write the following sets in the form of an interval
(i) `{x:x in R,2 ltxle5}`
(ii) `{x:x in R,-5ltxlt3}`
(iii) `{x:x in R,1 lt x lt 8}`
(iv) `{x : x in R, -7 lt x lt4}`

Answer

To express the given sets in the form of intervals, we will analyze each part of the question step by step.

### Step-by-Step Solution:

**(i)** The set is given as `{x : x in R, 2 < x ≤ 5}`.
- Here, \( x \) is greater than 2 but less than or equal to 5.
- Since 2 is not included, we use a round bracket (2).
- Since 5 is included, we use a square bracket [5].
- Therefore, the interval is: **(2, 5]**.

**(ii)** The set is given as `{x : x in R, -5 < x < 3}`.
- Here, \( x \) is greater than -5 and less than 3.
- Both -5 and 3 are not included, so we use round brackets for both.
- Therefore, the interval is: **(-5, 3)**.

**(iii)** The set is given as `{x : x in R, 1 < x < 8}`.
- Here, \( x \) is greater than 1 and less than 8.
- Both 1 and 8 are not included, so we use round brackets for both.
- Therefore, the interval is: **(1, 8)**.

**(iv)** The set is given as `{x : x in R, -7 < x < 4}`.
- Here, \( x \) is greater than -7 and less than 4.
- Both -7 and 4 are not included, so we use round brackets for both.
- Therefore, the interval is: **(-7, 4)**.

### Final Answer:
1. (2, 5]
2. (-5, 3)
3. (1, 8)
4. (-7, 4)