copyright © texas education agency, 20131 computer programming boolean logic

Copyright © Texas Education Agency, 2013 1

Computer Programming

Boolean Logic

What is Boolean Logic?

© UNT in partnership with TEA IT: [Computer Programming] - [Boolean Logic] 2

Boolean logic is a system for determining the truth of a statement (or expression) based on whether certain variables are true or false.

For example: In the statement, “I will go for a walk if it is sunny,” the decision is based on whether it is true that it is ‘sunny.’


Historical Note

George Boole (1815-1864) was an English mathematician who devised a system of symbols and equations to represent logical decisions.

Boolean Algebra was not widely used until the invention of computers. Boolean logic expressions are used to design electronic circuits and to represent decision-making in software

© UNT in partnership with TEA IT: [Computer Programming] - [Boolean Logic] 3Copyright © Texas Education Agency, 2013 3

How is Boolean Logic used?

A combination of conditions, variables, and operators are used to determine if an expression is True or False.

It can also be used to determine which elements can be members of a given set.


How are these categories different?

Brown-eyed AND Male

Brown-eyed OR Male


Who would be in these groups?

NOT male AND wearing jeans

NOT <16


Like Mathematics, Boolean logic has operators

Mathematic Operators + - x / =


Boolean Operators

&& ( AND )

|| ( OR )

! ( NOT )

Cheese || Pepperoni && !Anchovies


Like Math, Boolean logic has an order of operations

Mathematic Order of Operations is PEMDAS Parentheses first Exponents next Multiplication and Division Addition and Subtraction


Order of Boolean Operations

Parentheses are not operators, but indicate grouping, consider these first.

NOT (!) must be considered next.

AND ( && ) is considered next.

OR ( || ) is considered last.


!Tall && Blonde || Rich

1. Consider the NOT first. !Tall is short.

2. Consider the AND next. !Tall and Blonde, in other words, Short and Blonde.

3. Consider the OR next.

This person can be either Short and Blonde, or they can be Rich. They can also be Short, Blonde, and Rich.


Order of Operations

Parentheses first, then NOT (!) , then && , then ||

!Tall && Blonde || Rich

!(Tall && Blonde) || Rich

!Tall && !Blonde || Rich


Venn Diagrams

Venn Diagrams can be used to visualize Boolean expressions.


Venn Diagram


A B

A && B


Where is !A


A B


Where is A || B ?


A B


Truth Tables

Truth tables are used to evaluate possible combinations of variables and operators.


A || B (A OR B)


A B A || B

True True True

True False True

False True True

False False False


A && B (A AND B)


A B A && B

True True True

True False False

False True False

False False False


!A (NOT A)


A !A

True False

False True


!A || B (NOT A OR B)


A B !A || B

True True True

True False False

False True True

False False True


Check for Understanding

Determining the results of a Boolean expression is known as evaluating it.

All Boolean expressions evaluate to either True or False


Evaluate: What would be printed, A or B?

boolean blonde = false;

if ( blonde)

System.out.println(“A”);

if ( !blonde)

System.out.println(“B”);



boolean tall = false;

boolean male = true;

if ( male && tall)


if ( male || tall)




boolean x = false;

boolean y = true;

if ( x && y)


if ( !x && y)



Shade in A || !B


A B


Shade in A && !B


A B


Shade in !A && !B


A B


Will it print?

boolean x = true;

boolean y = false;

if ( x && !y)

System.out.print(“A”);


Will it print?

boolean x = true;

boolean y = false;

if (! x || y)

System.out.print(“A”);


With what you know…

Can you evaluate a boolean expression?


copyright © texas education agency, 20131 computer programming boolean logic

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