If `B={x:x=(2n-1)/(n+2), n in W and n lt 4} ` then B can be wirtten as

Options

A. `{6,(1)/(3),(2)/(4),(-1)/(2)}`
B. `{(-1)/(2),(1)/(3),(3)/(4),1}`
C. `{3,(-1)/(2),(3)/(4),(6)/(5)}`
D. `{(1)/(5),(1)/(3),(-1)/(2),1}`

Answer

To solve the problem, we need to find the set \( B \) defined by the expression \( x = \frac{2n - 1}{n + 2} \) where \( n \) is a whole number and \( n < 4 \).

### Step-by-step solution:

1. **Identify the values of \( n \)**:
Since \( n \) is a whole number and \( n < 4 \), the possible values for \( n \) are:
\[ n = 0, 1, 2, 3 \]

2. **Calculate \( x \) for each value of \( n \)**:
- For \( n = 0 \):
\[ x = \frac{2(0) - 1}{0 + 2} = \frac{-1}{2} = -\frac{1}{2} \]
- For \( n = 1 \):
\[ x = \frac{2(1) - 1}{1 + 2} = \frac{2 - 1}{3} = \frac{1}{3} \]
- For \( n = 2 \):
\[ x = \frac{2(2) - 1}{2 + 2} = \frac{4 - 1}{4} = \frac{3}{4} \]
- For \( n = 3 \):
\[ x = \frac{2(3) - 1}{3 + 2} = \frac{6 - 1}{5} = \frac{5}{5} = 1 \]

3. **Compile the values into set \( B \)**:
The values of \( x \) calculated for \( n = 0, 1, 2, 3 \) are:
\[ B = \left\{ -\frac{1}{2}, \frac{1}{3}, \frac{3}{4}, 1 \right\} \]

4. **Final representation of set \( B \)**:
Thus, the set \( B \) can be written as:
\[ B = \left\{ -\frac{1}{2}, \frac{1}{3}, \frac{3}{4}, 1 \right\} \]