1. Computer Programming
Boolean Logic

3. What is Boolean Logic?
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.’ 3
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4. Historical Note
George Boole ( ) 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. 4
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5. Use of Boolean Logic
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.
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6. How are these categories different?
Brown-eyed AND Male
Brown-eyed OR Male
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7. Who would be in these groups?
NOT male AND wearing jeans
NOT <16
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8. Like Mathematics, Boolean logic has operators
Mathematic Operators + - x / =
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9. Boolean Operators && ( AND ) || ( OR ) ! ( NOT )
Cheese || Pepperoni && !Anchovies
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10. Boolean logic has an order of operations
Mathematic Order of Operations is PEMDAS -
Parentheses first
Exponents next
Multiplication and Division
Addition and Subtraction.
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11. 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.
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12. !Tall && Blonde || Rich Consider the NOT first. !Tall is short.
Consider the AND next. !Tall and Blonde, in other words, Short and Blonde.
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.
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13. Order of Operations
Parentheses first, then NOT (!) , then && , then ||
!Tall && Blonde || Rich
!(Tall && Blonde) || Rich
!Tall && !Blonde || Rich
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14. Venn Diagrams
Venn Diagrams can be used to visualize Boolean expressions.
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15. Venn Diagram A B
A && B
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16. Where is !A A B
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17. Where is A || B ? A B
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18. Truth Tables
Truth tables are used to evaluate possible combinations of variables and operators.
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19. A || B (A OR B) A B
A || B
True
False
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20. A && B (A AND B) A B
A && B
True
False
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21. !A (NOT A) A !A
True
False
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22. !A || B (NOT A OR B) A B !A || B True False
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23. Check for Understanding
Determining the results of a Boolean expression is known as evaluating it. All Boolean expressions evaluate to either True or False.
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24. Evaluate: What would be printed, A or B?
boolean blonde = false;
if ( blonde)
System.out.println(“A”);
if ( !blonde)
System.out.println(“B”);
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25. Evaluate: What would be printed, A or B?
boolean tall = false;
boolean male = true;
if ( male && tall)
System.out.println(“A”);
if ( male || tall)
System.out.println(“B”);
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26. Evaluate: What would be printed, A or B?
boolean x = false;
boolean y = true;
if ( x && y)
System.out.println(“A”);
if ( !x && y)
System.out.println(“B”);
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27. Shade in A || !B A B
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28. Shade in A && !B A B
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29. Shade in !A && !B A B
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30. Will it print? boolean x = true; boolean y = false; if ( x && !y)
System.out.print(“A”);
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31. Will it print? boolean x = true; boolean y = false; if (! x || y)
System.out.print(“A”);
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32. With what you know… Can you evaluate a boolean expression?
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