Chapter 1.5, Problem 33E

In Exercises $21-42$, define the necessary symbols, rewrite the argument in symbolic form, and use a truth table to determine whether the argument is valid. If the argument is invalid, interpret the specific circumstances that cause the argument to be invalid.

$\begin{array}{l}\text{1. Drinking espresso is sufficient for not sleeping.}\\ \text{2. Not eating dessert is necessary for being on a diet.}\\ \text{3. Not eating dessert is sufficient for drinking espresso.}\\ \text{Therefore, not being on a diet is necessary for sleeping.}\end{array}$