If R is the set of real numbers and Q is the set of rational numbers, then what is `R- Q`?

Options

A. Set of rational numbers
B. Set of irrational numbers
C. Set of irrational numbers including `0`
D. None

Explanation

To solve the problem, we need to understand the sets involved:

1. **Identify the sets**:
- Let \( R \) be the set of all real numbers.
- Let \( Q \) be the set of all rational numbers.

2. **Understand the relationship between the sets**:
- The set of real numbers \( R \) can be expressed as the union of the set of rational numbers \( Q \) and the set of irrational numbers. This can be written as:
\[ R = Q \cup I \]
where \( I \) is the set of irrational numbers.

3. **Perform the set operation**:
- We need to find \( R - Q \), which represents the set of elements that are in \( R \) but not in \( Q \).
- Since \( R \) is composed of both rational and irrational numbers, removing the rational numbers \( Q \) from \( R \) will leave us with the irrational numbers \( I \).

4. **Conclusion**:
- Therefore, we can conclude that:
\[ R - Q = I \]
- This means that \( R - Q \) is the set of all irrational numbers.

### Final Answer:
\[ R - Q = \text{The set of all irrational numbers} \]