$(1)$ Read the following argument literally.

If you eat your dinner then you will get dessert.

You did not eat your dinner.

Therefore, you will not get dessert.

$($a$)$ Assign variable names to each component statement, di :$=$ "You eat your dinner," and de :$=$ "You will get dessert." Interpret the argument literally, then use a Truth Table to show the argument is invalid.

$($b$)$ The argument is invalid because we interpreted informal English literally. Reinterpret the informal English as what most likely the speaker actually meant. Then use a new Truth Table to show the argument is valid after all. $($Informal English, also known as Informal Language, is discussed on page $62.)$