Answer to Question #95022 in Discrete Mathematics for Gabriel

Question

What reads "the goods are are standard if and only if the goods are expensive"?

Answer 1

True conditional statement $p$ : if the goods are standard, then they are expensive.

True converse statement $q$ : if the goods are expensive, then they are standard.

Resulting biconditional statement: the goods are standard if and only if the goods are expensive.

$$p\iff q$$

This means that both $p$ and $q$ are true or else they are both false.

The biconditional $p$ if and only if $q$ is logically equivalent to saying $p$ implies $q$ and $q$ implies $p$ .

The$\ if\ and \ only \ if$ Chart:

$$\def\arraystretch{1.5} \begin{array}{c:c:c} p & q & p\ \ if\ and \ only \ if \ q \\ \hline T & T & T \\ \hdashline T & F & F \\ \hdashline F & T & F\\ \hdashline F & F & T \end{array}$$