Assertion (A) : Group-`13`-doped crystals of `Si` are called `p`-type semiconductors.
Reason (R ) : Positive holes are reasponsible for the semiconducting properties.

Options

A. If both `(A)` and `(R)` are correct, 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 both `(A)` is incorrect, but `(R)` is correct.

Answer

To solve the assertion and reason question, we need to analyze both statements and determine their correctness and relationship.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "Group-13-doped crystals of Si are called p-type semiconductors."
- Group 13 elements (like boron) have three valence electrons. When they are doped into silicon (which has four valence electrons), they create a deficiency of electrons (or holes) in the silicon lattice.

2. **Understanding the Reason (R)**:
- The reason states that "Positive holes are responsible for the semiconducting properties."
- In p-type semiconductors, the majority charge carriers are indeed positive holes. These holes allow for the conduction of electricity, as they can move through the lattice and facilitate current flow.

3. **Evaluating the Correctness of A and R**:
- Both statements are correct:
- A is correct because doping silicon with Group 13 elements does create p-type semiconductors.
- R is also correct because the presence of positive holes is what allows these p-type semiconductors to conduct electricity.

4. **Determining the Relationship**:
- R provides a valid explanation for A. The reason (R) explains why Group-13-doped silicon is classified as a p-type semiconductor: it is the positive holes that are responsible for the semiconducting properties.

5. **Conclusion**:
- Since both A and R are correct and R is the correct explanation of A, we conclude that the correct answer is:
- Both A and R are correct, and R is the correct explanation of A.

### Final Answer:
Both A and R are correct, and R is the correct explanation of A.

---