Negation of the conditional " if it rains then I shall go to school" is-

Options

A. It rains and I shall go to school
B. It rains and I shall not goto school
C. If does not rain and I shall go to school
D. None of these

Answer

To find the negation of the conditional statement "If it rains, then I shall go to school," we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components of the Conditional Statement**:
- Let \( p \) represent "It rains."
- Let \( q \) represent "I shall go to school."
- The conditional statement can be expressed as \( p \implies q \) (if \( p \) then \( q \)).

2. **Understand the Negation of a Conditional Statement**:
- The negation of the statement \( p \implies q \) is logically equivalent to \( p \land \neg q \).
- This means "It rains and I do not go to school."

3. **Express the Negation in Sentence Form**:
- The negation \( p \land \neg q \) translates to "It rains and I shall not go to school."

4. **Final Statement**:
- Therefore, the negation of the conditional statement "If it rains, then I shall go to school" is: "It rains and I shall not go to school."