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

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

example 1

(A  B)  (A  B) = ____

Venn Diagram: AB 1 2 3 4 (A  B)  (A  B)

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

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

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

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

(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

(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)

(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)

(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

(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

example 2

[A  ( B  A )]  [A  B ] = ____

Venn Diagram: AB 1 2 3 4 [A  ( B  A )]  [A  B ]

[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 1 2 3 4 [A  ( B  A )]  [A  B ] [A  (1,3  3,4)]  [A  B ]

[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 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 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 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 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 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 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 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 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 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 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 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

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