Conjuntos

Representa mediante diagramas de Venn:

U= [ 1,2,3,4,5,6,7,8,9,10,11,12,13……..36]

M= [2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36]

N= [3,6,9,12,15,18,21,24,27,30,33,36]

P= [1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35*]

M∩N = [6,12,18,24,36]

M∩P = [∅ ]

N∩P= [3,9,21,15,27]

M∩N∩P= [∅ ]

Representa mediante diagramas de Venn:

A=[ i n g e n i e r i a]

B= [ s I s t e m a s]

A ▲B=[ n g r s t]

A=[ n g r]

B= [ m s t]

U=[ingenieriasistemas]

A∩B=[i e a]

AUB=[ g n r I e a m s t]

Representa mediante diagramas de Venn:

M=[ 1 2 3 4]

N=[ 4 5]

M ▲N= [ 1 2 3 5]

M ∩N=[4]

U= [1 2 3 4 5]

A= [2,3]

N= [1,-2]

AXB= [2,1] [2,-2] [3,1] [3,-2]

Realiza la demostración gráfica del teorema de D’ Morgan para: (A ∩B)' = A'U B' paraello subraya el área correspondiente.

Primera parte: representa en cada conjunto A, B y el complemento de la intersección entre A yB:

Segunda parte de la igualdad A' U B': representa en cada conjunto A’, B’ y la unión entre ambos conjuntos

1. ((A∩B)´)´= (A´UB’)’= A∩B

2. (A’)’ ∩ (((B)’)’)= (A’)’ ∩ ((B’)’)= (A’)’ ∩ (B)= A ∩ B

3. (A’UA’) U B’= (A’) U B’= A∩ B

4. (A ∩∅)’ = (∅)’= ∅’=U

5. (A ∩∅’)’= (A ∩ U)’= A’

6. (A’ ∩ U’)’= AU U=U

7. (A ∩A)’ U (A’U A’)= (A)’ U (A’) = A’ U A’ = A’

8. (A U A’)’= (U)’= ∅

9. (A’ ∩ A’)’ U A’ = (A U A)’ U A’ = A’ U A’ = A’

10. (( A’)’ U U’)’ ∩ A’ = (A U U’)’ ∩ A’ = (U’)’ ∩ A’ = U ∩ A’= A’

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