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Write the negation of each of the disjun...

Write the negation of each of the disjunction:
Ram is in class X or Rina is in Class IX.

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To find the negation of the disjunction "Ram is in class X or Rina is in Class IX," we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Statements**: - Let \( P \): "Ram is in class X." - Let \( Q \): "Rina is in class IX." 2. **Formulate the Disjunction**: - The original statement is \( P \lor Q \) (P OR Q). 3. **Apply the Negation**: - The negation of a disjunction \( P \lor Q \) is given by De Morgan's Laws, which state that: \[ \neg(P \lor Q) \equiv \neg P \land \neg Q \] - This means that the negation of "P or Q" is equivalent to "not P and not Q". 4. **Negate Each Statement**: - Negate \( P \): "Ram is not in class X" (denoted as \( \neg P \)). - Negate \( Q \): "Rina is not in class IX" (denoted as \( \neg Q \)). 5. **Combine the Negated Statements**: - Using the conjunction (AND), we combine the negated statements: \[ \neg P \land \neg Q \] - This translates to: "Ram is not in class X and Rina is not in class IX." ### Final Answer: The negation of the statement "Ram is in class X or Rina is in Class IX" is: **"Ram is not in class X and Rina is not in class IX."** ---
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Knowledge Check

  • Negation of "Ram of in class X or Rashmi is in Class XII" is

    A
    Ram is not in class X but Rashmi is in Class XII
    B
    Ram is not in class X and Rashmi is not in Class XII
    C
    Either Ram is not in class X or Rashmi is not in class XII
    D
    None of the above
  • Negation of ''Monu is in class X or Anu is in class XII'' is

    A
    Monu is not in class X and Anu is in class XII
    B
    Monu is not in class X and Anu is not in class XII
    C
    Either Monu is not in class X or Anu is not in class XII
    D
    None of these
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