The negation of the statement:
"If Ludhiana is in Punjab, then Mumbai is in India"
the negation of p→q is ~(p→q)
The negation of the statement "If Ludhiana is in Punjab, then Mumbai is in India" would be "Ludhiana is in Punjab, but Mumbai is not in India."
To find the negation of a conditional statement, we have to negate both the hypothesis (the "if" part) and the conclusion (the "then" part) of the statement.
The original statement is: "If Ludhiana is in Punjab, then Mumbai is in India."
The hypothesis: "Ludhiana is in Punjab."
The conclusion: "Mumbai is in India."
To negate the hypothesis, we would say: "Ludhiana is not in Punjab."
To negate the conclusion, we would say: "Mumbai is not in India."
Putting it together, the negation of the original statement would be:
"Ludhiana is not in Punjab, or Mumbai is not in India."
So, the negation of the statement "If Ludhiana is in Punjab, then Mumbai is in India" is "Ludhiana is not in Punjab, or Mumbai is not in India."