Assertion (A): While the extraction of copper, one of the steps involved is
`Cu_(2)S+2Cu_(2)O to 6Cu+SO_(2)`
Reason (R): In this reaction `Cu_(2)S` is the reducing agent whereas `Cu_(2)O` is the oxidising agent.

Options

A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true.

Explanation

### Step-by-Step Solution:

1. **Understanding the Reaction**: The given reaction is:
\[ \text{Cu}_2\text{S} + 2\text{Cu}_2\text{O} \rightarrow 6\text{Cu} + \text{SO}_2 \]
This reaction is part of the extraction process of copper.

2. **Identifying Oxidation States**:
- In \(\text{Cu}_2\text{S}\), sulfur (S) has an oxidation state of -2. Therefore, the oxidation state of copper (Cu) can be calculated as follows:
\[ 2x - 2 = 0 \implies x = +1 \]
Thus, in \(\text{Cu}_2\text{S}\), copper is in the +1 oxidation state.
- In \(\text{Cu}_2\text{O}\), oxygen (O) has an oxidation state of -2. Therefore, the oxidation state of copper is:
\[ 2x - 2 = 0 \implies x = +1 \]
Thus, in \(\text{Cu}_2\text{O}\), copper is also in the +1 oxidation state.

3. **Determining Changes in Oxidation States**:
- In the products, elemental copper (Cu) has an oxidation state of 0.
- The sulfur in \(\text{SO}_2\) has an oxidation state of +4.

4. **Identifying Reducing and Oxidizing Agents**:
- A reducing agent is a substance that donates electrons and is oxidized in the process. Here, \(\text{Cu}_2\text{S}\) is oxidized to \(\text{Cu}\), indicating it is acting as a reducing agent.
- An oxidizing agent is a substance that accepts electrons and is reduced in the process. Here, \(\text{Cu}_2\text{O}\) is also reduced to \(\text{Cu}\), indicating it is acting as an oxidizing agent.

5. **Evaluating the Assertion and Reason**:
- **Assertion (A)**: The statement about the reaction being part of copper extraction is true.
- **Reason (R)**: The statement that \(\text{Cu}_2\text{S}\) is a reducing agent and \(\text{Cu}_2\text{O}\) is an oxidizing agent is also true.

6. **Conclusion**: Since both the assertion and the reason are true, the correct answer is that both statements are true.

### Final Answer:
- Assertion (A) is true.
- Reason (R) is true.
- Therefore, both A and R are correct.