SIMPLIFY using a Venn Digram or Laws of
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- Slides: 30
SIMPLIFY using a Venn Digram or Laws of Set Algebra Pamela Leutwyler
example 1
(A B) (A B ) = ____ Venn Diagram: A B 2 1 3 4 (A B) (A B )
(A B) (A B ) = ____ Venn Diagram: A B 2 1 3 4 (A B) (A B ) 1
(A B) (A B ) = ____ Venn Diagram: A B 2 1 3 4 (A B) (A B ) 1 (1, 2
(A B) (A B ) = ____ Venn Diagram: A B 2 1 3 4 (A B) (A B ) 1 (1, 2 2, 4)
(A B) (A B ) = ____ Venn Diagram: A B 1 2 3 4 (A B) (A B ) 1 (1, 2 2, 4) 1 2
(A B) (A B ) = ____ Venn Diagram: A B 1 2 3 4 (A B) (A B ) 1 (1, 2 2, 4) 1 1, 2 =A 2
(A B) (A B ) = ____ Venn Diagram: Laws of Set Algebra: : (A B) (A B ) A B 1 2 3 4 (A B) (A B ) 1 (1, 2 2, 4) 1 1, 2 =A 2
(A B) (A B ) = ____ Venn Diagram: Laws of Set Algebra: : (A B) (A B ) A B 1 2 Distributive law 3 A ( B B ) 4 (A B) (A B ) 1 (1, 2 2, 4) 1 1, 2 =A 2
(A B) (A B ) = ____ Venn Diagram: Laws of Set Algebra: : (A B) (A B ) A B 1 2 Distributive law 3 A ( B B ) 4 (A B) (A B ) 1 (1, 2 2, 4) 1 1, 2 =A 2 Complement Law A U
A (A B) (A B ) = ____ Venn Diagram: Laws of Set Algebra: : (A B) (A B ) A B 1 2 Distributive law 3 A ( B B ) 4 (A B) (A B ) 1 (1, 2 2, 4) 1 1, 2 =A 2 Complement Law A U Identity Law =A
example 2
[A ( B A )] [A B ] = ____ Venn Diagram: A B 2 1 3 4 [A ( B A )] [A B ]
[A ( B A )] [A B ] = ____ Venn Diagram: A B 2 1 3 4 [A ( B A )] [A B ] [A (1, 3 A )] [A B ]
[A ( B A )] [A B ] = ____ Venn Diagram: A B 2 1 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ]
[A ( B A )] [A B ] = ____ Venn Diagram: A B 2 1 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: A B 2 1 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: A B 2 1 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: A B 2 1 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ]
[A ( B A )] [A B ] = ____ Venn Diagram: A B 2 1 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3
[A ( B A )] [A B ] = ____ Venn Diagram: A B 2 1 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B
[A ( B A )] [A B ] = ____ Venn Diagram: Laws of Set Algebra: : [A ( B A )] [A B ] A Distributive Law B 2 1 [(A B) (A A )] [A B ] 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B
[A ( B A )] [A B ] = ____ Venn Diagram: Laws of Set Algebra: : [A ( B A )] [A B ] A Distributive Law B 2 1 [(A B) (A A )] [A B ] 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B [(A B) Complement Law Identity Law [(A B) ] [A B ]
[A ( B A )] [A B ] = ____ Venn Diagram: Laws of Set Algebra: : [A ( B A )] [A B ] A Distributive Law B 2 1 [(A B) (A A )] [A B ] 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B [(A B) Complement Law Identity Law [(A B) ] [A B ] [A B ] [A B ]
[A ( B A )] [A B ] = ____ Venn Diagram: Laws of Set Algebra: : [A ( B A )] [A B ] A Distributive Law B 2 1 [(A B) (A A )] [A B ] 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B [(A B) Complement Law Identity Law [(A B) ] [A B ] [A B ] [A B ] Distributive Law ( A A ) B
[A ( B A )] [A B ] = ____ Venn Diagram: Laws of Set Algebra: : [A ( B A )] [A B ] A Distributive Law B 2 1 [(A B) (A A )] [A B ] 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B [(A B) Complement Law Identity Law [(A B) ] [A B ] [A B ] [A B ] Distributive Law ( A A ) B Complement Law U B
B [A ( B A )] [A B ] = ____ Venn Diagram: Laws of Set Algebra: : [A ( B A )] [A B ] A Distributive Law B 2 1 [(A B) (A A )] [A B ] 3 4 [A ( B A )] [A B ] [A (1, 3 3, 4)] [A B ] [1, 2 (1, 3, 4)] [A B ] [ 1 ] [ 3 ] 1, 3 = B [(A B) Complement Law Identity Law [(A B) ] [A B ] [A B ] [A B ] Distributive Law ( A A ) B Complement Law U B Identity Law = B