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The problem asks to express the sentence "I'm late for class and the teacher will not be happy" in symbolic logic using the definitions provided.

We are given:
- \( p = \) "I'm late for class"
- \( q = \) "The teacher will be happy"

The sentence "I'm late for class and the teacher will not be happy" can be broken down into two parts:
1. "I'm late for class" → This corresponds to \( p \).
2. "The teacher will not be happy" → This corresponds to \( \neg q \) (the negation of \( q \)).

Now, combining these two using the logical "and" (denoted as \( \land \)):

The sentence in symbols is:  
\[ p \land \neg q \]

Let me know if you need any further explanation!

Here are five related questions:
1. What is the difference between conjunction (\( \land \)) and disjunction (\( \lor \)) in logic?
2. How would you negate the entire statement \( p \land \neg q \)?
3. How would you express the sentence "I'm late for class or the teacher will not be happy" in symbols?
4. What would the symbolic form of "The teacher will not be happy if I'm late for class" look like?
5. How would you express the opposite of the given statement, "I'm not late for class and the teacher will be happy"?

**Tip:** In symbolic logic, understanding the meaning of each operator (like \( \neg \), \( \land \), \( \lor \)) is essential for accurately translating between language and symbols.

Use the definitions of p and q to write 'I'm late for class and the teacher will not be happy' in symbols.

Learn how to translate the sentence 'I'm late for class and the teacher will not be happy' into logical symbols using propositional logic. This problem involves conjunction (∧) and negation (¬) and is suitable for high school students.

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