Page 30 - SM III Aritmetica 5to SEC

Aritmética 5° San Marcos

LEYES DISTRIBUTIVAS PARA LA UNIÓN Y LA INTERSECCIÓN

I. A  (B  C) = (A  B)  (A  C) II. A  (B  C) = (A  B)  (A  C)

Nota:

a. 2 conjuntos: b. 3 conjuntos

A B
A B

 n (A  B) = n(A) + n(B) – n(A  B) C
 n (A − B) = n(A) − n(A  B)
n(A  B  C) = n(A)+n(B)+n(C) – n(A  B) – n(A  C)
− n(B  C) + n(A  B  C)

c
COMPLEMENTO DE UN CONJUNTO: Símbolo: A’ , A , C A = {x/x  U  x  A}
U

U

A’ = C A = U – A = U  A’
A U

Ejemplos:

➢ Propiedades:
U = {x  Z / -2  x  6} = { –2, – 1, 0, 1, 2, 3, 4, 5, 6}
A = {x / 1  x 6, x es impar} = {1, 3, 5}
B = {x / 1 < x < 7, x es par} = {2, 4, 6}

a. A’ = {-2, -1, 0, 2, 4, 6}
b. B’ = {-2, -1, 0, 1, 3, 5}
c. (A  B)’ = ’ = U = {– 2, – 1 , 0, 1, 2, 3, 4, 5, 6}
d. (A  B)’ = { – 2 , – 1, 0}
e. (A’)’ = A = {1, 3, 5}
f. (B – A)’ = (B  A’)’ = B’  (A’)‘ = B’  A = {-2, -1, 0, 1, 3, 5}
g. (A − )’ = (A  ’)’ = A’  (’)’ = A’
h. A  A’ = 
i. ’ = U
j. U = 

Compendio -29-