# Boolean values

From GeoGebra Manual

You can use the Boolean variables *true* and *false* in GeoGebra. Just type, for example,
`a = true`

or `b = false`

into the Input Bar and press the Enter-key.

## Check Box and Arrow Keys

Free Boolean variables can be displayed as check boxes in the Graphics View (see tool Check Box Tool). After selecting a Boolean variable in the Algebra View you can use the arrow keys to change the value of the Boolean variable (see Manual Animation).

**Note:**You may also use Boolean variables like numbers (value 0 or 1). This allows you to use a checkbox as the dynamic speed of an animated slider allowing you to start and stop the animation. In this case, the animation button is only shown in the

*Graphics View*if there is also an animated slider with static (i.e. non-dynamic) speed.

## Operations

You can use the following operations for Boolean variables and conditions in GeoGebra by either selecting them from the list next to the Input Bar or by entering them using the keyboard:

Operation | List | Keyboard | Example | Object types |
---|---|---|---|---|

Equal | ≟ | == | a ≟ b or a == b | numbers, points, lines, conics a, b |

Unequal | ≠ | != | a ≠ b or a != b | numbers, points, lines, conics a, b |

Less than | < | a < b | numbers a, b | |

Greater than | > | a > b | numbers a, b | |

Less or equal than | ≤ | <= | a ≤ b or a <= b | numbers a, b |

Greater or equal than | ≥ | >= | a ≥ b or a >= b | numbers a, b |

And | ∧ | && | a ∧ b or a && b | Booleans a, b |

Or | ∨ | || | a ∨ b or a || b | Booleans a, b |

Not | ¬ | ! | ¬a or !a | Boolean a |

Parallel | ∥ | a ∥ b | lines a, b | |

Perpendicular | ⊥ | a ⊥ b | lines a, b | |

Belongs to | ∈ | a ∈ list1 | number a, list of numbers list1 |