Biconditional Operator

Type classification: this is a lesson resource.

Welcome! This is a lesson in the Introductory Discrete Mathematics for Computer Science course here at Wikiversity.

Previous lesson: Conditional Operator

Your Last Operator!

The biconditional operator looks like this: $\leftrightarrow$

It is a dyadic operator. You'll learn about what it does in the next section.

Compound Propositions and Logical Equivalence

Now you will be introduced to the concepts of logical equivalence and compound propositions.

• Compound propositions involve the assembly of multiple statements, using multiple operators.
• Logical equivalence means that the truth tables of two statements are the same.

The biconditional operator is sometimes called the "if and only if" operator. $p\leftrightarrow q$ = TRUE means that the truth values of p and q are the same. "You will see the notes for this class if and only if someone shows them to you" is an example of a biconditional statement.

1. If someone shows you the notes and you see them, the statement is true.
2. If someone shows you the notes and you do not see them, the biconditional statement is violated. Therefore, a value of "false" is returned.
3. If no one shows you the notes and you see them, the biconditional statement is violated. Therefore, a value of "false" is returned.
4. If no one shows you the notes and you do not see them, a value of true is returned.

• The biconditional statement $p\leftrightarrow q$ is logically equivalent to $\neg (p\oplus q)$!

Truth Table for the Biconditional

$p\,\!$	$q\,\!$	$p\leftrightarrow q$
T	T	T
T	F	F
F	T	F
F	F	T

Next Lesson

The next lesson is called Compound Propositions and Useful Rules.