Questions: Use the letters given to express the given compound statement in symbolic form. It is not snowing in Florida and it is snowing in Maine. t : It is snowing in Florida. r It is snowing in Maine.

Solution Steps

To express the given compound statement in symbolic form, we need to translate the English statement into logical symbols using the provided variables. The statement "It is not snowing in Florida and it is snowing in Maine" can be represented using logical operators. The negation of "It is snowing in Florida" is represented as $\sim t$, and "it is snowing in Maine" is represented as $r$. The conjunction "and" is represented by the logical operator $\wedge$. Therefore, the symbolic form of the statement is $\sim t \wedge r$.

The statement "It is not snowing in Florida and it is snowing in Maine" involves two logical components:

• \( t \): It is snowing in Florida.
• \( r \): It is snowing in Maine.

The statement "It is not snowing in Florida" is represented as \(\sim t\), where \(\sim\) denotes negation. The statement "and it is snowing in Maine" is represented as \(r\). The conjunction "and" is represented by the logical operator \(\wedge\).

Combine the logical components using the conjunction operator: \[ \sim t \wedge r \]

Given the values:

• \( t = \text{False} \) (It is not snowing in Florida)
• \( r = \text{True} \) (It is snowing in Maine)

The compound statement \(\sim t \wedge r\) evaluates to: \[ \text{True} \wedge \text{True} = \text{True} \]

Final Answer