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Negation of ''Monu is in class X or Anu ...

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

Text Solution

AI Generated Solution

The correct Answer is:
To find the negation of the statement "Monu is in class X or Anu is in class XII," we can follow these steps: ### Step 1: Identify the components of the statement Let: - \( p \): "Monu is in class X" - \( q \): "Anu is in class XII" The original statement can be expressed as: \[ p \lor q \] (where \( \lor \) represents "or"). ### Step 2: Write the negation of the statement The negation of the statement \( p \lor q \) can be expressed using De Morgan's Laws, which state that: \[ \neg(p \lor q) = \neg p \land \neg q \] (where \( \neg \) represents "not" and \( \land \) represents "and"). ### Step 3: Apply the negation to each component Now, we need to negate both \( p \) and \( q \): - \( \neg p \): "Monu is not in class X" - \( \neg q \): "Anu is not in class XII" ### Step 4: Combine the negations Using the result from De Morgan's Laws, we combine the negations: \[ \neg(p \lor q) = \neg p \land \neg q \] This translates to: "Monu is not in class X and Anu is not in class XII." ### Final Answer The negation of "Monu is in class X or Anu is in class XII" is: "Monu is not in class X and Anu is not in class XII." ---
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