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To write the statements in symbolic form using \( p \) and \( q \), we first interpret the meanings of \( p \) and \( q \) based on the provided information:

- \( p \): "It is Monday."
- \( q \): "There are students in the classroom."

### Symbolic Forms:

1. **Statement 1: "If it is Monday, then there are students in the classroom."**

   This is a conditional statement. In symbolic form, this is written as:

   \[
   p \rightarrow q
   \]
   Which means "If \( p \), then \( q \)."

2. **Statement 2: "If there are no students in the classroom, then it is not Monday."**

   This is also a conditional statement, but it involves the negation of both \( q \) and \( p \). In symbolic form, this is written as:

   \[
   \neg q \rightarrow \neg p
   \]
   Which means "If not \( q \), then not \( p \)."

Would you like more details on conditional statements or any other clarifications?

Here are 5 related questions to deepen your understanding:
1. How would you negate the statement \( p \rightarrow q \)?
2. What is the converse of \( p \rightarrow q \)?
3. What is the contrapositive of \( p \rightarrow q \)?
4. How would you express "There are no students in the classroom" using symbolic logic?
5. Can you give an example of a biconditional statement involving \( p \) and \( q \)?

**Tip**: In logical statements, the contrapositive of \( p \rightarrow q \) is always logically equivalent to the original statement!

Write each statement in symbolic form using p and q. p: It is Monday. q: There are students in the classroom. Statement 1: If it is Monday, then there are students in the classroom. Statement 2: If there are no students in the classroom, then it is not Monday.

Learn how to express logical statements using symbolic forms. This problem covers the use of conditional statements and negation in symbolic logic with real-world examples like 'It is Monday' and 'There are students in the classroom'. Suitable for high school students studying propositional logic.

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