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Boolean AlgebraResult in a True or False
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Named for
GeorgeBoole1815-1865
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Boolean Algebra• Mathematical expressions that results in
either true or false.• They can be joined to make more
complex Boolean expression using Boolean Operators like AND, OR, NOT.
• They are used to control if statements and loops. This means that Boolean Algebra is one of the cornerstones of computer science.
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&&
||
!
And
Or
Not
Some Java Symbols for you...
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Can you read this shirt now?
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Boolean Algebra evaluates to only two answers.
True False||
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Operator Meaning
> Greater than
>= Greater than or equal to
< Less than
<= Less than or equal to
== Equal to
!= Not equal to
.equals() Equal for strings
Relational Operators
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The variable num holds the value of 5.Are these true or false?
num > 6
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
F
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
F
T
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2F
T
T
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
F
T
T
F
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
!(num==3)
F
T
T
F
F
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
!(num==3)
F
T
T
F
F
T
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
!(num==3)
F
T
T
F
F
T
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
!(num==3)
F
T
T
F
F
T
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
!(num==3)
F
T
T
F
F
T
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The variable num holds the value of 5.Are these true or false?
num > 6
num >= 5
num != 6
num < 2
num == 4
!(num==3)
F
T
T
F
F
T
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Says: “Yes or no? I won’t
take anything else for an answer!”
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Would you like some cake && ice cream?
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Depending on what you give them, the kid is either happy or sad.
True False
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&& =
&& =
&& =
&& =
Where’s my ice cream?
Where’s my cake?
Where’s my cake and ice
cream?
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Value 1 Value 2 Answer
T && T = T
T && F = F
F && T = F
F && F = F
And Truth Table
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
If x is 4 and y is 7...
(x>3) && (x<9)
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
If x is 4 and y is 7...
(x>3) && (x<9)= (4>3) && (4<9)
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
If x is 4 and y is 7...
(x>3) && (x<9)= (4>3) && (4<9)= T && T
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
If x is 4 and y is 7...
(x>3) && (x<9)= (4>3) && (4<9)= T && T= T
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
If x is 4 and y is 7...
(x>3) && (x<9)= (4>3) && (4<9)= T && T= T
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What can go in the recycling bin?
Paper || Plastic
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|| =
|| =
|| =
|| =
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Value 1 Value 2 Answer
T || T = T
T || F = T
F || T = T
F || F = F
OR Truth Table
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
If x is 4 and y is 7...
(x==3) || (y>9)
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
If x is 4 and y is 7...
(x==3) || (y>9)= (4==3) || (7>9)
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
If x is 4 and y is 7...
(x==3) || (y>9)= (4==3) || (7>9)= F || F
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
If x is 4 and y is 7...
(x==3) || (y>9)= (4==3) || (7>9)= F || F= F
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! =
! =
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Value Answer
!T = F
!F = T
NOT Truth Table
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
Ans
!T = F
!F = T
If x is 4 and y is 7...
!(!(x<=7) && !(y!=9))
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Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
Ans
!T = F
!F = T
If x is 4 and y is 7...
!(!(x<=7) && !(y!=9))= !(!(4<=7) && !(7!=9))
![Page 44: Boolean Algebra - Gorski CompScigorskicompsci.ca/ICS3U/Unit1/ppt_BooleanAlgebra.pdf · Boole 1815-1865 && ||! And Or Not Some Java Symbols for you... Can you read this shirt now?](https://reader033.vdocuments.mx/reader033/viewer/2022050602/5fa96459bed86c0024784d7c/html5/thumbnails/44.jpg)
Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
Ans
!T = F
!F = T
If x is 4 and y is 7...
!(!(x<=7) && !(y!=9))= !(!(4<=7) && !(7!=9))= !(!T && !T)
![Page 45: Boolean Algebra - Gorski CompScigorskicompsci.ca/ICS3U/Unit1/ppt_BooleanAlgebra.pdf · Boole 1815-1865 && ||! And Or Not Some Java Symbols for you... Can you read this shirt now?](https://reader033.vdocuments.mx/reader033/viewer/2022050602/5fa96459bed86c0024784d7c/html5/thumbnails/45.jpg)
Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
Ans
!T = F
!F = T
If x is 4 and y is 7...
!(!(x<=7) && !(y!=9))= !(!(4<=7) && !(7!=9))= !(!T && !T)= !(F && F)
![Page 46: Boolean Algebra - Gorski CompScigorskicompsci.ca/ICS3U/Unit1/ppt_BooleanAlgebra.pdf · Boole 1815-1865 && ||! And Or Not Some Java Symbols for you... Can you read this shirt now?](https://reader033.vdocuments.mx/reader033/viewer/2022050602/5fa96459bed86c0024784d7c/html5/thumbnails/46.jpg)
Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
Ans
!T = F
!F = T
If x is 4 and y is 7...
!(!(x<=7) && !(y!=9))= !(!(4<=7) && !(7!=9))= !(!T && !T)= !(F && F)=!F
![Page 47: Boolean Algebra - Gorski CompScigorskicompsci.ca/ICS3U/Unit1/ppt_BooleanAlgebra.pdf · Boole 1815-1865 && ||! And Or Not Some Java Symbols for you... Can you read this shirt now?](https://reader033.vdocuments.mx/reader033/viewer/2022050602/5fa96459bed86c0024784d7c/html5/thumbnails/47.jpg)
Ans
T && T = T
T && F = F
F && T = F
F && F = F
Evaluate
Ans
T || T = T
T || F = T
F || T = T
F || F = F
Ans
!T = F
!F = T
If x is 4 and y is 7...
!(!(x<=7) && !(y!=9))= !(!(4<=7) && !(7!=9))= !(!T && !T)= !(F && F)=!F=T
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Some jokes.
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You can’t handle the truth!
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