Which of type of is used in following statements
p : A physical quantity is scalar or vector
q : A number is multiple of 5 or 25

Options

A. (i) Inclusive OR (ii) Exclusive OR
B. (i) Exclusive OR (ii) Inclusive OR
C. (i) Inclusive OR (ii) Inclusive OR
D. (i) Exclusive OR (ii) Exclusive OR

Answer

To determine the type of logical operation used in the given statements, we need to analyze each statement individually.

### Step-by-Step Solution:

1. **Identify the Statements**:
- Statement \( p \): "A physical quantity is scalar or vector."
- Statement \( q \): "A number is a multiple of 5 or 25."

2. **Analyze Statement \( p \)**:
- In statement \( p \), a physical quantity can either be a scalar or a vector, but not both at the same time.
- This means that if a quantity is a scalar, it cannot be a vector, and vice versa.
- Therefore, this statement represents an **exclusive or (XOR)** situation.

3. **Analyze Statement \( q \)**:
- In statement \( q \), a number can be a multiple of 5, a multiple of 25, or both.
- For example, the number 25 is a multiple of both 5 and 25.
- Thus, it is possible for both conditions to be true at the same time.
- Therefore, this statement represents an **inclusive or (OR)** situation.

4. **Conclusion**:
- Statement \( p \) uses an **exclusive or (XOR)**.
- Statement \( q \) uses an **inclusive or (OR)**.

### Final Answer:
- Statement \( p \): Exclusive or (XOR)
- Statement \( q \): Inclusive or (OR)

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