Boolean values

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. With Boolean variables you can e.g. define the conditional visibility of an object.

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, functions (needs CAS), planes, a, b
Not equal	≠	!=	a ≠ b or a != b	numbers, points, lines, conics, functions (needs CAS), planes 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
Exclusive or		Alt+	a ⊕ b	booleans a, b
Implication	→	->	a -> b	booleans a, b
Parallel	∥		a ∥ b	lines a, b
Perpendicular	⊥		a ⊥ b	lines a, b
Belongs to	∈		a ∈ list1	number a, list of numbers list1
Subset	⊆		list1 ⊆ list2	lists list1 and list2
Proper subset	⊂		list1 ⊂ list2	lists list1 and list2