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

Options

A. 4-Oxo-2, 3-dimethylpent-2-en-1-oic acid
B. 2-Carboxy-3-methylpent-2-en-3-one
C. 4-Carboxy-3-methylpent-3-en-2-one
D. 2,3-Dimethyl-4-oxo-pent-2-en-1-oic acid

Answer

To determine the IUPAC name of the given molecule, we will follow a systematic approach.

### Step-by-Step Solution:

1. **Identify the Functional Groups**:
The molecule contains a carboxylic acid group (-COOH) and a ketone group (C=O). The carboxylic acid has a higher priority in nomenclature than the ketone.

2. **Determine the Parent Chain**:
Since the carboxylic acid is the principal functional group, we will consider the longest carbon chain that includes this group. The longest chain contains 5 carbon atoms, making it a pentane.

3. **Number the Carbon Chain**:
We will number the carbon chain starting from the carboxylic acid end (which is carbon 1). The numbering will be as follows:
- C1: -COOH (carboxylic acid)
- C2: Alkene (double bond)
- C3: Methyl substituent
- C4: Ketone substituent
- C5: Methyl substituent

4. **Identify the Alkene**:
There is a double bond between C2 and C3. Since the double bond starts at carbon 2, we denote this as "pent-2-ene".

5. **Identify the Carboxylic Acid**:
The carboxylic acid is at carbon 1, so we denote this as "1-oic acid".

6. **Combine Alkene and Carboxylic Acid**:
The name so far is "pent-2-ene-1-oic acid". However, since the presence of the carboxylic acid takes precedence, we will replace the "ene" with "oic acid". Thus, it becomes "pent-2-ene-1-oic acid".

7. **Identify and Name the Substituents**:
- There are two methyl groups located at C2 and C3, which we denote as "2,3-dimethyl".
- There is a ketone (C=O) at C4, which we denote as "4-oxo".

8. **Combine All Parts**:
The full name will be constructed by combining the substituents and the parent name in alphabetical order:
- "2,3-dimethyl" comes before "4-oxo" (since 'D' comes before 'O' in the alphabet).
- The final IUPAC name is "2,3-dimethyl-4-oxo-pent-2-ene-1-oic acid".

### Final Answer:
The IUPAC name of the molecule is **2,3-dimethyl-4-oxo-pent-2-ene-1-oic acid**.