ÁLGEBRA DE CONJUNTOSWendy Lorena Motivar Cepeda

DADOS LOS CONJUNTOS:

A ={1,2,3,4,5}

B={6,7,8,9,0}

C={2,4,6,8}

D={3,5,7,9}

E={6,7,8}

F={Ø}

DESARROLLAR:

1,2,3,4,5A ∩ A = A

1,2,3,4,5A U A = A

A

A

1,2,3,4,5A ∩ Ø =Ø

1 2 3 4 5

Ø

A U Ø =A

Ø

A

FA

F

A ∩ U=A 6 7 8

9 01,2,3,4,5

A U

A U U=UU6 7 8

9 01,2,3,4,5

A

A ∩ B= B ∩ A 1 2 3

4 5

6 7 8

9 0

A U B= B U A 1 2 3

4 5

6 7 8

9 0

A B

A B

(AC)C = A

6 7 8

9 0AC = A

U

1,2,3,4,5

6 7 8

9 01,2,3,4,5

AU

(A ∩ B) ∩ C= A ∩(B ∩ C) → Ø

7

9

0

1 3 5

2 4 6 8

A B

C

7

9

0

1 3 5

2 4 6 8

A B

C

(A U B) U C= A U(B U C)

A ∩(B U C) = (A ∩ B) U (A ∩ C)

7 9

0

1 3

5

6 8

(B U C)

2 4

A ∩(B U C)

7 9

0

1 3

5

6 8

(A ∩ C)

(A ∩ B)

2 4

(A ∩ B) U (A ∩ C)

A B

C C

A B

AC U BC = (A ∩ B) C

U

2 4 6 8

A B

C

AC

BC

(A ∩ B) C

AC ∩ BC = (A U B) C → Ø

7

9

0

1 3 5

2 4 6 8

A B

C

U

A U (B ∩ C) = (A U B) ∩ (A U C)

7 9

0

1 3

5

6 82 4

7 9

0

1 3

5

6 82 4

(B ∩ C)

A U (B ∩ C)

(A U B)

(A U C)

(A U B) ∩ (A U C)

A B

C

A B

C

A ∩ B C A C A U B

1 2 3

4 5

6 7 8

9 0

A B

C \ (A ∩ B) = (C \ A) U (C \ B)

7 9

0

1 3

5

6 82 4

(A ∩ B)

C \ (A ∩ B)

7 9

0

1 3

5

6 82 4

(C \ A)

(C \ B)

(C \ A) U (C \ B)

A B

C

A B

C

C \ (A U B) = (C \ A) ∩ (C \ B)

7 9

0

1 3

5

6 82 4

(A U B)

C \ (A U B)

7 9

0

1 3

5

6 82 4

(C \ A)

(C \ B)

(C \ A) ∩(C \ B)

A B

C

A B

C

C \ (B \ A) = (A ∩ C) U (C \ B)

7 9

0

1 3

5

6 82 4

(B \ A)

C \ (B \ A)

7 9

0

1 3

5

6 82 4

(A ∩ C)

(C \ B)

(A ∩ C) U (C \ B)

A B

C

A B

C

(B \ A) ∩ C = (B ∩ C)\ A U = B ∩ (C \ A)

7 9 0

1 3

5

6 82 4

(B \ A)

(B \ A) ∩ C

7 9

0

1 3

5

6 82 4

7 9

0

1 3

5

6 82 4

A B

C

A B

C

A B

C

(B ∩ C)

(B ∩ C)\ A

(C \ A)

B ∩ (C \ A)

(B \ A) U C = (B U C)\ (A \ C)

7 9

0

1 3

5

6 82 4

(B \ A)

(B \ A) U C

7 9

0

1 3

5

6 82 4

(B U C)

(A \ C)

(B U C)\ (A \ C)

A B

C

A B

C

A \ A = Ø

1,2,3,

4,5 1,2,

3,

4,5 1,2,

3,

4,5

Ø \ A = Ø A \ Ø = A

A

A F

A F

A \ B = A ∩ BC

1 2 3

4 5

6 7 8

9 0

1 2 3

4 5

6 7 8

9 0

A BU

BA

A \ B BC

A ∩ BC

(B \ A)C = A U BC

1 2 3

4 5

6 7 8

9 0

1 2 3

4 5

6 7 8

9 0

A BU

BA

B \ A BC

A U BC

U

(B \ A)C

6 7 8

9 0

AU

1,2,3,4,5

U \ A = AC

6 7 8

9 0

AU

1,2,3,4,5

A \ U = Ø