What is relation between following compounds
`CH_(3)-CH_(2)-underset(CN)underset(|)(CH)-CH_(2)-COOH`
` & CH_(3)-underset(CN)underset(|)(CH)-CH_(2)-CH_(2)-COOH`

Options

A. positional isomers
B. chain isomers
C. Metamers
D. None of these

Answer

To determine the relationship between the two given compounds, we need to analyze their structures and identify their molecular formulas, as well as the position of their functional groups.

### Step-by-step Solution:

1. **Identify the Functional Groups**:
- Both compounds contain a carboxylic acid group (-COOH) and a cyano group (-CN). The carboxylic acid is the higher priority functional group.

2. **Number the Carbon Chain**:
- Start numbering from the carboxylic acid group (COOH) since it has the highest priority.
- For the first compound (let's call it Compound A):
- COOH (1), CH2 (2), CH (3), CH2 (4), CN (5).
- For the second compound (let's call it Compound B):
- COOH (1), CH2 (2), CH2 (3), CH (4), CN (5).

3. **Count the Carbon Atoms**:
- Both compounds have a total of 5 carbon atoms in their longest chain, including the carbon in the carboxylic acid group.

4. **Determine the Molecular Formula**:
- For both compounds, counting the atoms gives:
- Carbon (C): 6
- Hydrogen (H): 9
- Oxygen (O): 2
- Nitrogen (N): 1
- Therefore, the molecular formula for both compounds is C6H9O2N.

5. **Identify the Type of Isomerism**:
- Since both compounds have the same molecular formula and the same number of carbon atoms in the parent chain, they cannot be chain isomers (which require a difference in the carbon skeleton).
- Instead, they differ in the position of the cyano group (CN). In Compound A, the cyano group is on the 4th carbon, while in Compound B, it is on the 3rd carbon.

6. **Conclusion**:
- The two compounds are **position isomers** because they have the same molecular formula but differ in the position of the cyano group.