The contrapositive of statement 'If Chandigarh is capital of Punjab , then Chandigarh is in India" is

Options

A. if Chandigarh is not in India, then Chandigarh is not the of punjab
B. if Chandigarh is in India is India, the chandigarh is not the capital of Punjab
C. if Chandigarh is notcapital of Punjab , then Chandigarh is not capital of India.
D. If Chandigarh is not Capital of Punjab, then Chandigarh is not is India.

Explanation

To find the contrapositive of the statement "If Chandigarh is the capital of Punjab, then Chandigarh is in India," we can follow these steps:

### Step 1: Identify the components of the statement
The given statement is in the form of an implication (if-then statement):
- Let \( P \) be the statement "Chandigarh is the capital of Punjab."
- Let \( Q \) be the statement "Chandigarh is in India."

### Step 2: Write the implication
The implication can be written as:
- If \( P \), then \( Q \) (i.e., \( P \implies Q \))

### Step 3: Formulate the contrapositive
The contrapositive of an implication \( P \implies Q \) is given by:
- If not \( Q \), then not \( P \) (i.e., \( \neg Q \implies \neg P \))

### Step 4: Apply the negation to the statements
Now, we need to negate both statements:
- Negation of \( Q \): "Chandigarh is not in India" (i.e., \( \neg Q \))
- Negation of \( P \): "Chandigarh is not the capital of Punjab" (i.e., \( \neg P \))

### Step 5: Write the contrapositive statement
Now we can write the contrapositive:
- If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.

### Final Answer
The contrapositive of the statement "If Chandigarh is the capital of Punjab, then Chandigarh is in India" is:
**"If Chandigarh is not in India, then Chandigarh is not the capital of Punjab."**

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