Assertion`:` `q+w` is a state function.
Reason`:` sum of two path function is state function.

Options

A. If both Assertion & Reason are True & the Reason is a correct explanation of the Assertion.
B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertiion.
C. If Assertion is True but the Reason is False.
D. If both Assertion & Reason are False

Explanation

To solve the question, we need to analyze the assertion and reason given:

**Assertion:** \( q + w \) is a state function.
**Reason:** The sum of two path functions is a state function.

### Step-by-Step Solution:

1. **Define State Functions and Path Functions:**
- A **state function** is a property whose value depends only on the state of the system, not on how that state was reached. Examples include internal energy, enthalpy, and pressure.
- A **path function** is a property that depends on the path taken to reach a particular state. Examples include heat (q) and work (w).

2. **Understanding the Assertion:**
- The assertion states that \( q + w \) is a state function. To evaluate this, we refer to the first law of thermodynamics, which states:
\[ \Delta U = q + w \]
where \( \Delta U \) is the change in internal energy, which is a state function.

3. **Evaluating the Reason:**
- The reason states that the sum of two path functions is a state function. In this case, both \( q \) (heat) and \( w \) (work) are path functions. However, when we add them together, we obtain \( \Delta U \), which is indeed a state function.

4. **Conclusion:**
- Since \( \Delta U \) is a state function and is equal to \( q + w \), the assertion is correct. Additionally, the reason correctly explains why the assertion is true, as it describes the relationship between path functions and state functions.

5. **Final Answer:**
- Both the assertion and reason are true, and the reason is the correct explanation for the assertion.