In which of the following examples an inclusive or is· used

Options

A. Two lines intersect at a point or are parallel
B. Students can take French or Spanish as their third language
C. To apply for a driving licence, you should have a ration card or a passport·
D. All integers are positive or negative

Answer

To determine which example uses an inclusive "or," we need to understand the definitions of inclusive and exclusive "or."

1. **Definitions**:
- **Inclusive "or"**: This means that at least one of the conditions can be true, and both can also be true. For example, "A or B" means A is true, B is true, or both A and B are true.
- **Exclusive "or"**: This means that only one of the conditions can be true, but not both. For example, "A or B" means A is true, B is true, but not both A and B can be true simultaneously.

2. **Analyzing the Options**:
- **Option 1**: "Two lines intersect at a point or two lines are parallel."
- Here, if two lines intersect, they cannot be parallel at the same time. Thus, this is an exclusive "or."
- **Option 2**: "Students can take French or Spanish as their third language."
- In this case, students must choose one language; they cannot take both simultaneously. Therefore, this is also an exclusive "or."
- **Option 3**: "To apply for a driving license, you should have a ration card or a passport."
- Here, having a ration card or a passport means that a person can have either one or both. Thus, this is an inclusive "or."
- **Option 4**: "All integers are positive or negative."
- An integer cannot be both positive and negative at the same time. Thus, this is an exclusive "or."

3. **Conclusion**:
- The only option that represents an inclusive "or" is **Option 3**: "To apply for a driving license, you should have a ration card or a passport."

### Final Answer:
**Option 3**: To apply for a driving license, you should have a ration card or a passport.

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