Statement-1 . The IUPAC name of the compound
`{:(CH_(2)=CH-CH=CH-CH-C-=CH),(" |"),(" "CH=CH_(2)),(" 5-ethynylhepta-1,3,6-triene"):}`
Statement-2. While numbering the carbon chain triple bond is given preference over the double bond.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is False

Explanation

To solve the question, we will analyze both statements provided regarding the IUPAC naming of the compound and the rules for numbering carbon chains with multiple bonds.

### Step-by-Step Solution:

1. **Identify the Compound Structure**:
The compound given is `CH2=CH-CH=CH-CH-C≡CH` with an ethyl group `CH=CH2` attached. This compound has both double and triple bonds.

2. **Count the Carbon Atoms**:
The main carbon chain has 7 carbon atoms (from the structure provided).

3. **Determine the Position of the Double and Triple Bonds**:
The compound has:
- Double bonds at positions 1, 3, and 6.
- A triple bond at position 5.

4. **IUPAC Naming Rules**:
According to IUPAC nomenclature rules, when numbering the carbon chain, the double bond is given preference over the triple bond. Therefore, we start numbering from the end of the chain that gives the first double bond the lowest possible number.

5. **Numbering the Carbon Chain**:
Starting from the left:
- C1: CH2 (double bond)
- C2: CH (double bond)
- C3: CH (double bond)
- C4: CH (single bond)
- C5: C (triple bond)
- C6: CH2
- C7: CH2 (ethyl group)

The correct numbering gives the double bonds the lowest possible numbers.

6. **Final IUPAC Name**:
The correct IUPAC name should be `5-ethylhepta-1,3,6-triene`, as the double bonds are prioritized in the naming.

7. **Evaluate Statement 1**:
Statement 1 claims the name is `5-ethynylhepta-1,3,6-triene`. This is incorrect because the correct name is `5-ethylhepta-1,3,6-triene`.

8. **Evaluate Statement 2**:
Statement 2 claims that while numbering the carbon chain, the triple bond is given preference over the double bond. This is also incorrect, as the double bond is prioritized over the triple bond.

9. **Conclusion**:
Both statements are false.

### Final Answer:
Both Statement 1 and Statement 2 are false.