Question

Translate the following statement using symbols: “The sky is cloudy and the temperature is not warm.” Let s represent “The sky is cloudy,” and let w represent “The temperature is warm.”

Answer 1

To translate the statement “The sky is cloudy and the temperature is not warm” using symbols, you can represent it as follows:

Let \( s \) = "The sky is cloudy"
Let \( w \) = "The temperature is warm"

The phrase "the temperature is not warm" can be expressed as \( \neg w \), which means "not w."

So, the entire statement can be represented in symbols as:

\[ s \land \neg w \]

Here, \( \land \) represents "and." Thus, the complete translation is \( s \land \neg w \).