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SIMPLIFY using a Venn Digram or Laws of Set Algebra Pamela Leutwyler.

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Presentation on theme: "SIMPLIFY using a Venn Digram or Laws of Set Algebra Pamela Leutwyler."— Presentation transcript:

1 SIMPLIFY using a Venn Digram or Laws of Set Algebra Pamela Leutwyler

2 example 1

3 (A  B)  (A  B) = ____

4 Venn Diagram: AB (A  B)  (A  B)

5 (A  B)  (A  B) = ____ Venn Diagram: AB (A  B)  (A  B) 1

6 (A  B)  (A  B) = ____ Venn Diagram: AB (A  B)  (A  B) 1  (1,2

7 (A  B)  (A  B) = ____ Venn Diagram: 4 (A  B)  (A  B) 1  (1,2  2,4) AB 1 2 3

8 (A  B)  (A  B) = ____ Venn Diagram: AB (A  B)  (A  B) 1  (1,2  2,4) 1  2

9 (A  B)  (A  B) = ____ Venn Diagram: AB (A  B)  (A  B) 1  (1,2  2,4) 1  2 1, 2 =A

10 (A  B)  (A  B) = ____ Venn Diagram: AB (A  B)  (A  B) 1  (1,2  2,4) 1  2 1, 2 =A Laws of Set Algebra:: (A  B)  (A  B)

11 (A  B)  (A  B) = ____ Venn Diagram: AB (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)

12 (A  B)  (A  B) = ____ Venn Diagram: AB (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

13 (A  B)  (A  B) = ____ Venn Diagram: AB (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

14 example 2

15 [A  ( B  A )]  [A  B ] = ____

16 Venn Diagram: AB [A  ( B  A )]  [A  B ]

17 [A  ( B  A )]  [A  B ] = ____ Venn Diagram: AB [A  ( B  A )]  [A  B ] [A  (1,3  A )]  [A  B ]

18 [A  ( B  A )]  [A  B ] = ____ Venn Diagram: AB [A  ( B  A )]  [A  B ] [A  (1,3  3,4)]  [A  B ]

19 [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 ]

20 [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 ]

21 [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 ]

22 [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 ]

23 [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

24 [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

25 [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

26 [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

27 [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 ]

28 [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

29 [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

30 [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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