Write the following sets in tabular form :
(i) `{:x : x = (2n)/(n+2), n in W` and `n lt 3`}
(ii) `{x : x = 5y-3, y in Z` and `-2 le y lt 2`}
(iii) `{x : x in W " and " 8x + 5 lt 23}`

Answer

To write the given sets in tabular form, we will evaluate each set based on the conditions provided.

### Step-by-Step Solution:

**(i)** The first set is given as:
\[ \{ x : x = \frac{2n}{n+2}, n \in W \text{ and } n < 3 \} \]
Where \( W \) is the set of whole numbers. The whole numbers less than 3 are \( n = 0, 1, 2 \).

1. **Substituting \( n = 0 \)**:
\[ x = \frac{2(0)}{0 + 2} = \frac{0}{2} = 0 \]

2. **Substituting \( n = 1 \)**:
\[ x = \frac{2(1)}{1 + 2} = \frac{2}{3} \]

3. **Substituting \( n = 2 \)**:
\[ x = \frac{2(2)}{2 + 2} = \frac{4}{4} = 1 \]

Thus, the first set in tabular form is:
\[ \{ 0, \frac{2}{3}, 1 \} \]

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**(ii)** The second set is given as:
\[ \{ x : x = 5y - 3, y \in Z \text{ and } -2 \leq y < 2 \} \]
Where \( Z \) is the set of integers. The values of \( y \) that satisfy the condition are \( y = -2, -1, 0, 1 \).

1. **Substituting \( y = -2 \)**:
\[ x = 5(-2) - 3 = -10 - 3 = -13 \]

2. **Substituting \( y = -1 \)**:
\[ x = 5(-1) - 3 = -5 - 3 = -8 \]

3. **Substituting \( y = 0 \)**:
\[ x = 5(0) - 3 = 0 - 3 = -3 \]

4. **Substituting \( y = 1 \)**:
\[ x = 5(1) - 3 = 5 - 3 = 2 \]

Thus, the second set in tabular form is:
\[ \{ -13, -8, -3, 2 \} \]

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**(iii)** The third set is given as:
\[ \{ x : x \in W \text{ and } 8x + 5 < 23 \} \]
We first solve the inequality:
\[ 8x + 5 < 23 \]
Subtracting 5 from both sides:
\[ 8x < 18 \]
Dividing by 8:
\[ x < \frac{18}{8} = 2.25 \]
Since \( x \) must be a whole number, the possible values are \( 0, 1, 2 \).

Thus, the third set in tabular form is:
\[ \{ 0, 1, 2 \} \]

### Final Answer:
The sets in tabular form are:
1. \( \{ 0, \frac{2}{3}, 1 \} \)
2. \( \{ -13, -8, -3, 2 \} \)
3. \( \{ 0, 1, 2 \} \)