Write each of the following statements in symbolic form and determine the truth value. 
A square is not a rectangle and 321 is not divisible by 3. 

Let's break down the given statement and write it in symbolic form.

### Statement: "A square is not a rectangle and 321 is not divisible by 3."

We can assign the following propositions:
- Let \( p \) represent "A square is a rectangle."
- Let \( q \) represent "321 is divisible by 3."

The original statement is a negation of both propositions with the conjunction "and." So, we can express this in symbolic form as:
\[
\neg p \land \neg q
\]

### Truth value:
1. **Is a square a rectangle?**  
   A square **is** a specific type of rectangle (since it has four right angles and opposite sides that are equal). Therefore, \( p \) is **true**, and \( \neg p \) is **false**.

2. **Is 321 divisible by 3?**  
   To check if 321 is divisible by 3, we sum its digits:  
   \( 3 + 2 + 1 = 6 \), and since 6 is divisible by 3, \( 321 \) is divisible by 3. Hence, \( q \) is **true**, and \( \neg q \) is **false**.

Since both \( \neg p \) and \( \neg q \) are false, the conjunction \( \neg p \land \neg q \) is **false**.

### Conclusion:
- **Symbolic form:** \( \neg p \land \neg q \)
- **Truth value:** **False**

Would you like further explanation or have any questions?

Here are 5 related questions:
1. What does the truth table of conjunction (AND) look like?
2. How do we define a rectangle mathematically?
3. What is the divisibility rule for 3?
4. How can we express a conditional statement in symbolic logic?
5. Can a proposition and its negation ever be true at the same time?

**Tip:** When using negations in logic, be careful to consider both the original statement and its opposite meaning.

Write each of the following statements in symbolic form and determine the truth value. A square is not a rectangle and 321 is not divisible by 3.

This page breaks down a logic problem where students must express the statement 'A square is not a rectangle and 321 is not divisible by 3' in symbolic form and determine its truth value. Concepts include propositional logic, negation, conjunction, and divisibility rules. Suitable for Grades 9-12.

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