Question:
Negation of “Ram is in Class X or Rashmi is in Class XII” is
Negation of “Ram is in Class X or Rashmi is in Class XII” is
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For negating OR statements, use De Morgan's law: \( \neg(p \, \text{OR} \, q) \equiv \neg p \, \text{AND} \, \neg q \).
Updated On: Apr 22, 2026
- Ram is not in Class X but Rashmi is in Class XII
- Ram is not in Class X but Rashmi is in Class XII
- Either Ram is not in Class X or Rashmi is not in class XII
- None of these
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The Correct Option is D
Solution and Explanation
Step 1: Identify the original statement.
The original statement is: \[ \text{“Ram is in Class X or Rashmi is in Class XII”} \] This is a logical OR statement.
Step 2: Apply negation to the OR statement.
The negation of an OR statement is given by De Morgan's law. De Morgan's law states that: \[ \neg(p \, \text{OR} \, q) \equiv \neg p \, \text{AND} \, \neg q \] Thus, the negation of the statement “Ram is in Class X or Rashmi is in Class XII” is: \[ \neg(\text{Ram is in Class X}) \, \text{AND} \, \neg(\text{Rashmi is in Class XII}) \] This simplifies to: \[ \text{Ram is not in Class X and Rashmi is not in Class XII} \]
Step 3: Conclusion.
Thus, the negation of the original statement is “Ram is not in Class X and Rashmi is not in Class XII,” which does not match any of the given options exactly. Therefore, the correct answer is option (D), “None of these.”
The original statement is: \[ \text{“Ram is in Class X or Rashmi is in Class XII”} \] This is a logical OR statement.
Step 2: Apply negation to the OR statement.
The negation of an OR statement is given by De Morgan's law. De Morgan's law states that: \[ \neg(p \, \text{OR} \, q) \equiv \neg p \, \text{AND} \, \neg q \] Thus, the negation of the statement “Ram is in Class X or Rashmi is in Class XII” is: \[ \neg(\text{Ram is in Class X}) \, \text{AND} \, \neg(\text{Rashmi is in Class XII}) \] This simplifies to: \[ \text{Ram is not in Class X and Rashmi is not in Class XII} \]
Step 3: Conclusion.
Thus, the negation of the original statement is “Ram is not in Class X and Rashmi is not in Class XII,” which does not match any of the given options exactly. Therefore, the correct answer is option (D), “None of these.”
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