True or False

2. Basic Types: Booleans

True or False

The first built-in Python type we will discuss are the booleans #\mathtt{\text{True}}# and #\mathtt{\text{False}}#.

In computer science, a boolean is a datatype that has one of two possible values: true or false. It is intended to represent the two truth values used in logic.

Booleans as numbers

The two possible values of a boolean in Python are the keywords #\color{#F5871F} {\mathtt{\text{True}}}# and #\color{#F5871F} {\mathtt{\text{False}}}#. However, the #\color{#4271ae} {\mathtt{\text{bool}}}# datatype actually inherits from the #\color{#4271ae} {\mathtt{\text{int}}}# type. Therefore, #\color{#F5871F} {\mathtt{\text{True}}}# and #\color{#F5871F} {\mathtt{\text{False}}}# can be seen as a layer of abstraction over the values a boolean actually represents: the integers #\color{#F5871F} {\mathtt{\text{1}}}# and #\color{#F5871F} {\mathtt{\text{0}}}#, meaning that booleans are actually a numeric datatype. As a result, booleans also support mathematical operators.

>>> 1 or 0

>>> 1 and 1

>>> True + True

In Python, the booleans #\mathtt{\text{True}}# and #\mathtt{\text{False}}# are the only two possible instances of the #\color{#4271ae} {\mathtt{\text{bool}}}# type. The #\color{#4271ae}{\mathtt{\text{bool}}}# type supports a few logical operators that mimic basic logic. Logical operators can be formalised as functions with one or two inputs that return a boolean themselves. The input can be any valid expression that results in a boolean when evaluated.

Logical operators

Operator	Name	Usage	Returns
#\mathtt{or}#	Disjunction	#\mathtt{\text{x}}# #\mathtt{or}# #\mathtt{\text{y}}#	Returns #\mathtt{\text{True}}# if either #\mathtt{\text{x}}# or #\mathtt{\text{y}}# or both are #\mathtt{\text{True}}#, otherwise #\mathtt{\text{False}}#.
#\mathtt{and}#	Conjunction	#\mathtt{\text{x}}# #\mathtt{and}# #\mathtt{\text{y}}#	Returns #\mathtt{\text{True}}# if both #\mathtt{\text{x}}# and #\mathtt{\text{y}}# are #\mathtt{\text{True}}#, otherwise #\mathtt{\text{False}}#.
#\mathtt{not}#	Negation	#\mathtt{not}# #\mathtt{\text{x}}#	Returns #\mathtt{\text{True}}# if #\mathtt{\text{x}}# is #\mathtt{\text{False}}#, otherwise #\mathtt{\text{False}}#.

Truth tables

The function of the three logical operators can also be summarised in truth tables. A truth table is a technique commonly used in the field of logic to evaluate expressions for different conditions by charting the output for all possible input combinations. These tables give a clearer indication of the behaviour of the logical operators.

	#\mathtt{or}#
#\mathtt{x}#	#\mathtt{y}#	#\mathtt{x}# #\mathtt{or}# #\mathtt{y}#
#\mathtt{\text{False}}#	#\mathtt{\text{False}}#	#\mathtt{\text{False}}#
#\mathtt{\text{False}}#	#\mathtt{\text{True}}#	#\mathtt{\text{True}}#
#\mathtt{\text{True}}#	#\mathtt{\text{False}}#	#\mathtt{\text{True}}#
#\mathtt{\text{True}}#	#\mathtt{\text{True}}#	#\mathtt{\text{True}}#

	#\mathtt{and}#
#\mathtt{x}#	#\mathtt{y}#	#\mathtt{x}# #\mathtt{and}# #\mathtt{y}#
#\mathtt{\text{False}}#	#\mathtt{\text{False}}#	#\mathtt{\text{False}}#
#\mathtt{\text{False}}#	#\mathtt{\text{True}}#	#\mathtt{\text{False}}#
#\mathtt{\text{True}}#	#\mathtt{\text{False}}#	#\mathtt{\text{False}}#
#\mathtt{\text{True}}#	#\mathtt{\text{True}}#	#\mathtt{\text{True}}#

	#\mathtt{not}#
#\mathtt{x}#		#\mathtt{not}# #\mathtt{x}#
#\mathtt{\text{False}}#		#\mathtt{\text{True}}#
#\mathtt{\text{True}}#		#\mathtt{\text{False}}#

Here, the #\mathtt{x}# and #\mathtt{y}# columns represent the possible inputs for the expression. The third column shows the output for that specific input.

You might be wondering why there aren't more such operators. The answer is actually quite simple; they are not needed. These three operators can create any other boolean function when combined. In fact, even just #\mathtt{\text{and}}# and #\mathtt{\text{not}}# suffice for functional completeness. The logical operators can be combined with booleans to form logical expressions that result in booleans:

>>> True or False

True

>>> True and True

True

>>> not False

True