# Biconditional Operator

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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![edit | edit source]

The **biconditional operator** looks like this:

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

## Compound Propositions and Logical Equivalence[edit | edit source]

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. = 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 is logically equivalent to !

## Truth Table for the Biconditional[edit | edit source]

T | T | T |

T | F | F |

F | T | F |

F | F | T |

## Next Lesson[edit | edit source]

The next lesson is called Compound Propositions and Useful Rules.