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SIMPLIFY using a Venn Digram or Laws of Set Algebra Pamela Leutwyler
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example 1
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(A B) (A B) = ____
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Venn Diagram: AB 1 2 3 4 (A B) (A B)
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2
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(A B) (A B) = ____ Venn Diagram: 4 (A B) (A B) 1 (1,2 2,4) AB 1 2 3
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2 2,4) 1 2
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2 2,4) 1 2 1, 2 =A
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2 2,4) 1 2 1, 2 =A Laws of Set Algebra:: (A B) (A B)
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2 2,4) 1 2 1, 2 =A Laws of Set Algebra:: (A B) (A B) Distributive law A ( B B)
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2 2,4) 1 2 1, 2 =A Laws of Set Algebra:: (A B) (A B) Distributive law A ( B B) Complement Law A U
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(A B) (A B) = ____ Venn Diagram: AB 1 2 3 4 (A B) (A B) 1 (1,2 2,4) 1 2 1, 2 =A Laws of Set Algebra:: (A B) (A B) Distributive law A ( B B) Complement Law A U Identity Law =A A
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example 2
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[A ( B A )] [A B ] = ____
![[A ( B A )] [A B ] = ____](http://images.slideplayer.com/10/2764686/slides/slide_15.jpg "[A ( B A )] [A B ] = ____")
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Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ]
![Venn Diagram: AB [A ( B A )] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_16.jpg "Venn Diagram: AB [A ( B A )] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 A )] [A B ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 A )] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_17.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 A )] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_18.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [A (1,3,4)] [A B ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [A (1,3,4)] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_19.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [A (1,3,4)] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_20.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_21.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]](http://images.slideplayer.com/10/2764686/slides/slide_22.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3](http://images.slideplayer.com/10/2764686/slides/slide_23.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B](http://images.slideplayer.com/10/2764686/slides/slide_24.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law](http://images.slideplayer.com/10/2764686/slides/slide_25.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law](http://images.slideplayer.com/10/2764686/slides/slide_26.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ]
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ]](http://images.slideplayer.com/10/2764686/slides/slide_27.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ]")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law](http://images.slideplayer.com/10/2764686/slides/slide_28.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law U B Complement Law
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law U B Complement Law](http://images.slideplayer.com/10/2764686/slides/slide_29.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law U B Complement Law")
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[A ( B A )] [A B ] = ____ Venn Diagram: AB 1 2 3 4 [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law U B Complement Law = B Identity Law B
![[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law U B Complement Law = B Identity Law B](http://images.slideplayer.com/10/2764686/slides/slide_30.jpg "[A ( B A )] [A B ] = ____ Venn Diagram: AB [A ( B A )] [A B ] [A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ] 1, 3 = B Laws of Set Algebra:: [A ( B A )] [A B ] [(A B) (A A)] [A B ] Distributive Law [(A B) ] [A B ] [(A B) ] [A B ] Complement Law Identity Law [A B ] [A B ] ( A A ) B Distributive Law U B Complement Law = B Identity Law B")
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