For each $($sub$)-$question, please provide detailed explanations to your answer. Otherwise, you will recieve a Zero.

$(10$ points$)$ Truth table

Write the truth table for the proposition not$(r$notq$)vv(p^{{?}^{?}}$notr$).$

Solution:

$(10$ points$)$ Translating English to Propositional Logic

$($a$)$ Using $c$ for $"$it is cold" and $d$ for $"$it is dry," write $"$It is neither cold nor dry" in symbols.

$($b$)$ Using $c$ for $"$it is cold" and $r$ for $"$it is rainy," write $"$It is rainy if it is not cold" in symbols.

$($c$)$ Using $c$ for $"$it is cold" and $w$ for $"$it is windy," write $"$To be windy it is necessary that it be cold" in symbols.

$($d$)$ Using $c$ for $"$it is cold," $r$ for $"$it is rainy," and $w$ for $"$it is windy," write $"$It is rainy only if it is windy and cold" in symbols.

Solution: