Let p and q represent the following simple​ statements:
​p: It is Tuesday
.
​q: It is snowing outside
.
​r: It is time to sleep
.
Write the following compound statement in its symbolic form.
It is time to sleep
​, 
if and only if it is Tuesday
 
and it is not snowing outside
.
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Part 1
Write the symbolic form of the statement below.
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Let's define the simple statements based on your given conditions:

- \( p \): It is Tuesday.
- \( q \): It is snowing outside.
- \( r \): It is time to sleep.

Now, the compound statement is:

> It is time to sleep if and only if it is Tuesday and it is not snowing outside.

This can be written symbolically as:

\[
r \leftrightarrow (p \land \neg q)
\]

Here:
- \( r \leftrightarrow \) represents "if and only if."
- \( p \land \neg q \) represents "it is Tuesday and it is not snowing outside."

Would you like further details on how this works logically?

---

Here are 5 related questions for you to consider:

1. How would you write the statement "If it is snowing outside, then it is not time to sleep" in symbolic form?
2. What is the symbolic form of "It is Tuesday or it is snowing outside, but it is not time to sleep"?
3. Can you simplify the expression \( (p \lor q) \land (r \leftrightarrow q) \)?
4. What is the truth table for the expression \( r \leftrightarrow (p \land \neg q) \)?
5. How do you prove that \( (p \land \neg q) \rightarrow r \) is logically equivalent to the original statement?

**Tip**: When translating compound statements into symbolic form, always break them down into individual conditions and clearly identify the logical connectors.

Let p and q represent the following simple statements: p: It is Tuesday. q: It is snowing outside. r: It is time to sleep. Write the following compound statement in its symbolic form. It is time to sleep, if and only if it is Tuesday and it is not snowing outside.

Explore how to write the symbolic form of the statement 'It is time to sleep, if and only if it is Tuesday and it is not snowing outside'. Learn about logical biconditionals, conjunctions, and negations, suitable for students in Grades 9-12.

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