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If R is the set of real numbers and Q i...

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

A

Set of rational numbers

B

Set of irrational numbers

C

Set of irrational numbers including `0`

D

None

Text Solution

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The correct Answer is:
To solve the problem, we need to determine what the set \( R - Q \) represents, where \( R \) is the set of real numbers and \( Q \) is the set of rational numbers. ### Step-by-Step Solution: 1. **Understanding the Sets**: - The set \( R \) includes all real numbers. Real numbers consist of both rational and irrational numbers. - The set \( Q \) includes all rational numbers, which can be expressed as the quotient of two integers (where the denominator is not zero). 2. **Identifying the Complement**: - When we subtract the set of rational numbers \( Q \) from the set of real numbers \( R \), we are left with the numbers that are in \( R \) but not in \( Q \). 3. **Finding \( R - Q \)**: - Since \( R \) contains both rational and irrational numbers, and \( Q \) contains only rational numbers, the subtraction \( R - Q \) will remove all rational numbers from \( R \). - Therefore, the remaining numbers will be the irrational numbers. 4. **Conclusion**: - Thus, we can conclude that \( R - Q \) is the set of irrational numbers. ### Final Answer: \[ R - Q = \text{Set of Irrational Numbers} \]
To solve the problem, we need to determine what the set \( R - Q \) represents, where \( R \) is the set of real numbers and \( Q \) is the set of rational numbers. ### Step-by-Step Solution: 1. **Understanding the Sets**: - The set \( R \) includes all real numbers. Real numbers consist of both rational and irrational numbers. - The set \( Q \) includes all rational numbers, which can be expressed as the quotient of two integers (where the denominator is not zero). ...
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