Assertion : `underset("3-carbethoxy- 2-butenoic acid.")(CH-underset(COOC_(2)H_(5))underset(|)(C)=CH-COOH)`
Reason: Principal functional group gets lowest number followed by double bond or triple bond.

Options

A. a. If both assertion and reason are true and reason is the correct explanation of assertion
B. b. If both assertion and reason are true but reason is not the correct explanation of assertion
C. c. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze the assertion and reason provided regarding the IUPAC naming of the compound.

### Step-by-Step Solution

1. **Identify the Compound Structure**:
The compound given is 3-carbethoxy-2-butenoic acid, which can be represented as:
\[ \text{CH}_3-\text{C}(\text{COOC}_2\text{H}_5)=\text{C}(\text{COOH})-\text{C} \]
Here, we have a carboxylic acid group (-COOH) and an ester group (-COOC2H5).

2. **Determine the Principal Functional Group**:
In IUPAC nomenclature, the principal functional group is the one that takes precedence in numbering. In this case, the carboxylic acid (-COOH) is the principal functional group.

3. **Number the Carbon Chain**:
We need to number the carbon chain starting from the end closest to the principal functional group (the carboxylic acid). The numbering will be as follows:
- C1: -COOH (carboxylic acid)
- C2: -C=C- (double bond)
- C3: -COOC2H5 (ester group)
- C4: -CH3 (methyl group)

4. **Assign Numbers to Functional Groups**:
Based on the numbering:
- The carboxylic acid is at position 1.
- The double bond is at position 2.
- The ester is at position 3.

5. **Construct the IUPAC Name**:
According to the IUPAC naming conventions:
- The name is constructed by stating the substituents and their positions followed by the principal functional group.
- The correct IUPAC name is 3-carbethoxy-2-butenoic acid.

6. **Evaluate the Assertion and Reason**:
- **Assertion**: The compound is correctly named as 3-carbethoxy-2-butenoic acid. This is true.
- **Reason**: The principal functional group (carboxylic acid) gets the lowest number followed by the double bond. This is also true.

7. **Conclusion**:
Since both the assertion and reason are true, and the reason correctly explains the assertion, the final conclusion is that the answer is option A.