Question

Let p and q be the propositions “The total amount is discounted” and “The items have been packed,” respectively. Express each of these compound propositions as an English sentence.

Answer 1

Since we have been given that  p and q are the propositions “The total amount is discounted” and “The items have been packed,” respectively,

Then

$\lnot$ p: The total amount is not discounted

$\lnot$ q: The items have not been packed

p$\iff$q : The total amount is discounted if and only if the items have been packed

$\lnot$ p$\implies\lnot$ q : If the total amount is not discounted then the items have not been packed.