Which type of OR is used in following pair of statements
(i) Afunction is onto or one - one
(ii) A function is even or odd

Options

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

Answer

To determine the type of OR used in the given statements, we need to analyze the nature of the statements provided.

### Step-by-step Solution:

1. **Understanding the Statements**:
- The first statement is: "A function is onto or one-one."
- The second statement is: "A function is even or odd."

2. **Analyzing the First Statement**:
- A function can be onto (surjective), one-one (injective), or both.
- This means that if a function is onto, it does not exclude the possibility of it also being one-one. Therefore, both conditions can be true simultaneously.

3. **Analyzing the Second Statement**:
- A function can be even, odd, or neither, but it cannot be both even and odd at the same time.
- Thus, if a function is even, it cannot be odd, and vice versa. This means that if one condition is true, the other must be false.

4. **Identifying the Type of OR**:
- The first statement represents an **inclusive OR** because both conditions can be true at the same time.
- The second statement represents an **exclusive OR** because both conditions cannot be true simultaneously.

5. **Conclusion**:
- Therefore, the first statement uses **inclusive OR**, and the second statement uses **exclusive OR**.

### Final Answer:
- The first statement uses **inclusive OR**, and the second statement uses **exclusive OR**.

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