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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 B12 3
4
(A B) (A B)
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1 (1,2
(A B) (A B) = ____
Venn Diagram:
4
(A B) (A B)
1 (1,22,4)
A B12 3
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1 (1,22,4)
1 2
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1 (1,22,4)
1 2
1 , 2
=A
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1 (1,22,4)
1 2
1 , 2
=A
Laws of Set Algebra::
(A B) (A B)
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1 (1,22,4)
1 2
1 , 2
=A
Laws of Set Algebra::
(A B) (A B) Distributive law
A ( B B)
(A B) (A B) = ____
Venn Diagram:
A B12 3
4
(A B) (A B)
1 (1,22,4)
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:
A B12 3
4
(A B) (A B)
1 (1,22,4)
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 ] = ____
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 3
4
[A ( B A )] [A B ]
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 3
4
[A ( B A )] [A B ]
[A (1,3 A )] [A B ]
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 3
4
[A ( B A )] [A B ]
[A (1,3 3,4)] [A B ]
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 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 B12 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 B12 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 B12 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:
A B12 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:
A B12 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:
A B12 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 ]
[(AB) (A A)] [A B ]
Distributive Law
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 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 ]
[(AB) (A A)] [A B ]
Distributive Law
[(AB) ] [A B ]
[(AB) ] [A B ]
Complement Law
Identity Law
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 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 ]
[(AB) (A A)] [A B ]
Distributive Law
[(AB) ] [A B ]
[(AB) ] [A B ]
Complement Law
Identity Law
[A B ] [A B ]
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 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 ]
[(AB) (A A)] [A B ]
Distributive Law
[(AB) ] [A B ]
[(AB) ] [A B ]
Complement Law
Identity Law
[A B ] [A B ]
( A A ) B Distributive Law
[A ( B A )] [A B ] = ____
Venn Diagram:
A B12 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 ]
[(AB) (A A)] [A B ]
Distributive Law
[(AB) ] [A B ]
[(AB) ] [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:
A B12 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 ]
[(AB) (A A)] [A B ]
Distributive Law
[(AB) ] [A B ]
[(AB) ] [A B ]
Complement Law
Identity Law
[A B ] [A B ]
( A A ) B Distributive Law
U B Complement Law
= B Identity Law
B
