Which of the following compound statement contains inclusive OR
p : `sqrt(35)` is a rational or an irrational number
q : 12 is an even or irrational number
r : To apply for post paid mobile connection you should have voter I- card or driving licence

Options

A. p only
B. q only
C. r only
D. All

Answer

To determine which of the given compound statements contains an inclusive OR, we need to analyze each statement based on the definition of inclusive OR. An inclusive OR means that at least one of the statements can be true, and both can also be true at the same time.

Let's analyze each statement step by step:

1. **Statement p**: "sqrt(35) is a rational or an irrational number."
- Here, we know that the square root of 35 is an irrational number. The statement presents two options: rational or irrational. Since sqrt(35) can only be one of these (not both), this does not satisfy the condition of inclusive OR. Therefore, this statement is not an inclusive OR.

2. **Statement q**: "12 is an even or irrational number."
- We know that 12 is an even number, but it is not an irrational number. Similar to the previous statement, this presents two options, but only one can be true at a time. Hence, this statement also does not satisfy the condition of inclusive OR. Therefore, this statement is not an inclusive OR.

3. **Statement r**: "To apply for postpaid mobile connection you should have a voter ID card or driving license."
- In this case, having a voter ID card or a driving license means that either one can be true, or both can be true. A person can apply with just a voter ID, just a driving license, or with both. This satisfies the condition of inclusive OR because at least one of the options can be true, and both can also be true. Therefore, this statement is an inclusive OR.

Based on the analysis:

- **Conclusion**: The statement that contains an inclusive OR is **Statement r**: "To apply for postpaid mobile connection you should have a voter ID card or driving license."