The given task asks for the symbolic representation of a compound statement based on the definitions of $p$, $q$, and $r$:

• $p$: It is snowing outside.
• $q$: It is cold.
• $r$: It is cloudy.

The compound statement is:
"If it is not snowing outside, then it is not cold and it is not cloudy."

Solution:

1. "If it is not snowing outside" translates to $\neg p$.
2. "It is not cold" translates to $\neg q$.
3. "It is not cloudy" translates to $\neg r$.
4. "It is not cold and it is not cloudy" is $\neg q \land \neg r$.
5. The entire compound statement, using the "if-then" logic ($\rightarrow$), becomes:
   $\neg p \rightarrow (\neg q \land \neg r)$

Final Answer:

The symbolic form is:
$\neg p \rightarrow (\neg q \land \neg r)$

Let me know if you need more clarification or a deeper explanation!

Related Questions:

1. What does $\rightarrow$ mean in logic, and how does it work?
2. Can the statement $\neg p \rightarrow (\neg q \land \neg r)$ be written in a different but equivalent form?
3. What is the truth table for this compound statement?
4. How does the "and" ($\land$) operator function when combined with negation?
5. How can we convert compound statements into their English equivalents?

Tip:

Always remember that in logic, $\neg$ (negation) reverses the truth value of a statement, and $\rightarrow$ means "if-then," where the statement is false only when the first part is true and the second part is false.