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SIMPLIFY using

SIMPLIFY using. a Venn Digram or Laws of Set Algebra. Pamela Leutwyler. example 1. (A  B)  (A  B) = ____. (A  B)  (A  B) = ____. Venn Diagram:. A. B. 1. 3. 2. 4. (A  B)  (A  B) . (A  B)  (A  B) = ____. Venn Diagram:. A. B. 1. 3. 2. 4.

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SIMPLIFY using

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  1. SIMPLIFY using a Venn Digram orLaws of Set Algebra Pamela Leutwyler

  2. example 1

  3. (A  B)  (A B) = ____

  4. (A  B)  (A B) = ____ Venn Diagram: A B 1 3 2 4 (A  B)  (A B)

  5. (A  B)  (A B) = ____ Venn Diagram: A B 1 3 2 4 (A  B)  (A B) 1

  6. (A  B)  (A B) = ____ Venn Diagram: A B 1 3 2 4 (A  B)  (A B) 1  (1,2

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

  8. (A  B)  (A B) = ____ Venn Diagram: A B 1 3 2 4 (A  B)  (A B) 1  (1,22,4) 1  2

  9. (A  B)  (A B) = ____ Venn Diagram: A B 1 3 2 4 (A  B)  (A B) 1  (1,22,4) 1  2 1 , 2 =A

  10. (A  B)  (A B) = ____ Venn Diagram: Laws of Set Algebra:: (A  B)  (A B) A B 1 3 2 4 (A  B)  (A B) 1  (1,22,4) 1  2 1 , 2 =A

  11. (A  B)  (A B) = ____ Venn Diagram: Laws of Set Algebra:: (A  B) (A B) A B Distributive law 1 3 2 A  ( B  B) 4 (A  B)  (A B) 1  (1,22,4) 1  2 1 , 2 =A

  12. (A  B)  (A B) = ____ Venn Diagram: Laws of Set Algebra:: (A  B)  (A B) A B Distributive law 1 3 2 A  ( B  B) 4 Complement Law A  U (A  B)  (A B) 1  (1,22,4) 1  2 1 , 2 =A

  13. A (A  B)  (A B) = ____ Venn Diagram: Laws of Set Algebra:: (A  B)  (A B) A B Distributive law 1 3 2 A  ( B  B) 4 Complement Law A  U (A  B)  (A B) Identity Law 1  (1,22,4) =A 1  2 1 , 2 =A

  14. example 2

  15. [A  ( B  A )]  [A  B ] = ____

  16. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: A B 1 3 2 4 [A  ( B  A )]  [A  B ]

  17. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: A B 1 3 2 4 [A  ( B  A )]  [A  B ] [A (1,3  A )]  [A  B ]

  18. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: A B 1 3 2 4 [A  ( B  A )]  [A  B ] [A (1,3  3,4)]  [A  B ]

  19. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: A B 1 3 2 4 [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: A B 1 3 2 4 [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: A B 1 3 2 4 [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: A B 1 3 2 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 ]

  23. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: A B 1 3 2 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

  24. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: A B 1 3 2 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

  25. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: Laws of Set Algebra:: [A  ( B  A )] [A  B ] Distributive Law A B 1 3 [(AB) (A  A)] [A  B ] 2 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

  26. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: Laws of Set Algebra:: [A  ( B  A )]  [A  B ] Distributive Law A B 1 3 [(AB) (A  A)]  [A  B ] 2 Complement Law 4 [(AB)   ]  [A  B ] Identity Law [A  ( B  A )]  [A  B ] [(AB) ]  [A  B ] [A (1,3  3,4)]  [A  B ] [1,2 (1,3,4)]  [A  B ] [ 1 ]  [A  B ] [ 1 ]  [ 3 ] 1, 3 = B

  27. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: Laws of Set Algebra:: [A  ( B  A )]  [A  B ] Distributive Law A B 1 3 [(AB) (A  A)]  [A  B ] 2 Complement Law 4 [(AB)   ]  [A  B ] Identity Law [A  ( B  A )]  [A  B ] [(AB) ]  [A  B ] [A  B ]  [A  B ] [A (1,3  3,4)]  [A  B ] [1,2 (1,3,4)]  [A  B ] [ 1 ]  [A  B ] [ 1 ]  [ 3 ] 1, 3 = B

  28. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: Laws of Set Algebra:: [A  ( B  A )]  [A  B ] Distributive Law A B 1 3 [(AB) (A  A)]  [A  B ] 2 Complement Law 4 [(AB)   ]  [A  B ] Identity Law [A  ( B  A )]  [A  B ] [(AB) ]  [A  B ] [A  B]  [A  B ] [A (1,3  3,4)]  [A  B ] Distributive Law [1,2 (1,3,4)]  [A  B ] ( A  A  )  B [ 1 ]  [A  B ] [ 1 ]  [ 3 ] 1, 3 = B

  29. [A  ( B  A )]  [A  B ] = ____ Venn Diagram: Laws of Set Algebra:: [A  ( B  A )]  [A  B ] Distributive Law A B 1 3 [(AB) (A  A)]  [A  B ] 2 Complement Law 4 [(AB)   ]  [A  B ] Identity Law [A  ( B  A )]  [A  B ] [(AB) ]  [A  B ] [A  B ]  [A  B ] [A (1,3  3,4)]  [A  B ] Distributive Law [1,2 (1,3,4)]  [A  B ] ( A  A  )  B [ 1 ]  [A  B ] Complement Law U B [ 1 ]  [ 3 ] 1, 3 = B

  30. B [A  ( B  A )]  [A  B ] = ____ Venn Diagram: Laws of Set Algebra:: [A  ( B  A )]  [A  B ] Distributive Law A B 1 3 [(AB) (A  A)]  [A  B ] 2 Complement Law 4 [(AB)   ]  [A  B ] Identity Law [A  ( B  A )]  [A  B ] [(AB) ]  [A  B ] [A  B ]  [A  B ] [A (1,3  3,4)]  [A  B ] Distributive Law [1,2 (1,3,4)]  [A  B ] ( A  A  )  B [ 1 ]  [A  B ] Complement Law U B [ 1 ]  [ 3 ] Identity Law = B 1, 3 = B

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