Write the negation of the followingstatement : 2If it is raining, then the game is cancelled

To negate the statement "If it is raining, then the game is cancelled," we will follow the logical principles of negation.

1. Identify the Components of the Statement

The statement can be broken down into two parts:

• P: It is raining.
• Q: The game is cancelled.

The original statement is in the form of a conditional: $P \rightarrow Q$.

2. Formulate the Negation

The negation of a conditional statement $P \rightarrow Q$ is given by the expression: $\neg (P \rightarrow Q)$ This can be simplified using the implication equivalence: $P \rightarrow Q \equiv \neg P \lor Q$ Thus, its negation is: $\neg (\neg P \lor Q)$ Using De Morgan's laws, this simplifies to: $P \land \neg Q$

3. Write the Negated Statement

The negation of the original statement translates to: "It is raining and the game is not cancelled."

Final Answer

The negation of the statement "If it is raining, then the game is cancelled" is: "It is raining and the game is not cancelled."