# Biconditional Operator

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Previous lesson: Conditional Operator

## Contents

## Your Last Operator!

The **biconditional operator** looks like this: [math]\leftrightarrow[/math]

It is a diadic 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. [math]p \leftrightarrow q[/math] = 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.

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

- The biconditional statement [math]p \leftrightarrow q[/math] is logically equivalent to [math]\neg(p \oplus q)[/math]!

## Truth Table for the Biconditional

[math]p \,\![/math] | [math]q \,\![/math] | [math]p \leftrightarrow q[/math] |
---|---|---|

T | T | T |

T | F | F |

F | T | F |

F | F | T |

## Next Lesson

The next lesson is called Compound Propositions and Useful Rules.