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 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 UIdentity 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