The IUPAC name of moleucle:
`CH_3-overset(O)overset(||)(C)-underset(CH_3)underset(|)(C)=underset(CH_2)underset(|)(C)-overset(O)overset(||)(C)-OH ` is

Options

A. 4-oxo - 2,3-dimethylpent - 2 - en - 1 oi`c^()` acid
B. 2-carboxy - 3 - methypent - 2 - en - 3 - one
C. 4-carboxy-3methylpent - 3- en -2 - one
D. 2,3-dimethyl-4 oxo pent - 2 - en - 1 - oic acid

Explanation

To determine the IUPAC name of the given molecule, we will follow the systematic approach for naming organic compounds.

### Step-by-Step Solution:

1. **Identify the Longest Carbon Chain**:
- The first step is to identify the longest continuous carbon chain in the molecule. In this case, the longest chain consists of 5 carbon atoms.
- **Hint**: Look for the longest unbroken chain of carbon atoms to determine the root name.

2. **Determine the Root Name**:
- Since the longest chain has 5 carbon atoms, the root name is "pent".
- **Hint**: The root name corresponds to the number of carbon atoms in the longest chain (e.g., "pent" for 5).

3. **Identify Functional Groups**:
- The molecule contains a carboxylic acid group (-COOH) and a ketone group (C=O). The carboxylic acid group has the highest priority.
- **Hint**: Functional groups have different priorities; carboxylic acids take precedence over ketones.

4. **Number the Carbon Chain**:
- Number the carbon chain starting from the end nearest to the carboxylic acid group. This gives the carboxylic carbon the number 1.
- The numbering will be:
- C1: -COOH (carboxylic acid)
- C2: C=O (ketone)
- C3: CH
- C4: CH
- C5: CH3
- **Hint**: Always number the chain to give the highest priority functional group the lowest possible number.

5. **Identify Substituents**:
- There are two methyl groups attached to the second and third carbon atoms.
- **Hint**: Substituents are named and their positions indicated by numbers.

6. **Construct the Name**:
- Combine the information:
- The substituents are "2,3-dimethyl".
- The root name is "pent".
- The functional groups are "4-oxo" (the ketone) and "1-oic" (the carboxylic acid).
- The full name is: **4-oxo-2,3-dimethylpentanoic acid**.
- **Hint**: The order of naming is: substituents, root name, functional groups.

### Final Answer:
The IUPAC name of the molecule is **4-oxo-2,3-dimethylpentanoic acid**.