Assertion (A): Addition of `Ag^(o+)` ions to a mixture of aqueous `NaCI` and `NaBr` solution will first precipitate `AgBr` rather than `AgCI`.
Reason (R) : `K_(sp) AgCI lt K_(sp) of AgBr`.

Options

A. If both (A) and (R) are correc, and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect, but (R) is correct.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when `Ag^+` ions are added to a mixture of `NaCl` and `NaBr` solutions, `AgBr` will precipitate first before `AgCl`.
- We need to determine whether this statement is true or false.

2. **Understanding the Reason**:
- The reason given is that the solubility product constant (`Ksp`) of `AgCl` is less than that of `AgBr`.
- We need to verify if this reason is correct and if it supports the assertion.

3. **Comparing Ksp Values**:
- The solubility product constant (`Ksp`) indicates how soluble a salt is in water. A lower `Ksp` value means the salt is less soluble and will precipitate more readily.
- For the salts in question:
- `Ksp(AgCl)` < `Ksp(AgBr)` means that `AgCl` is less soluble than `AgBr`.

4. **Analyzing Precipitation**:
- When `Ag^+` ions are introduced to the solution, they will react with the halide ions present (`Cl^-` and `Br^-`).
- The precipitation will occur based on which salt has a lower `Ksp`, meaning it will precipitate first.

5. **Determining the Correct Precipitation Order**:
- Since `AgBr` has a higher `Ksp` than `AgCl`, it is more soluble and will precipitate after `AgCl`.
- Therefore, the assertion that `AgBr` precipitates first is **false**.

6. **Conclusion**:
- The assertion is incorrect because `AgCl` will precipitate first due to its lower `Ksp` value compared to `AgBr`.
- The reason provided is also incorrect because it states the opposite of the actual relationship between the `Ksp` values.

### Final Answer:
- Both the assertion and the reason are false.