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

Options

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

Answer

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 original statement
The original statement is:
- "Monu is in class X or Anu is in class XII."

### Step 2: Understand the logical structure
The statement is a disjunction (an "or" statement), which can be represented as:
- Let P: "Monu is in class X"
- Let Q: "Anu is in class XII"
- The statement can be written as: P ∨ Q

### Step 3: Apply the negation rule
The negation of a disjunction (P ∨ Q) is given by De Morgan's laws, which states:
- ¬(P ∨ Q) = ¬P ∧ ¬Q

This means that the negation of "P or Q" is "not P and not Q."

### Step 4: Negate each component
Now we negate each part:
- ¬P: "Monu is not in class X"
- ¬Q: "Anu is not in class XII"

### Step 5: Combine the negated components
Using the results from Step 4, we combine them using "and":
- The negation of the original statement is:
"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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