calculo











1. Sea el conjunto universal U = { x ϵ N / x ≤ 10 } y los conjuntos :

A = {x ϵ N / x2 ˂ 10} ; B = { x ϵ N / x3 ≤ 15 } ; C = { 2x/x ϵ N ˄ x ≤ 7 }

D = { x ϵ N /x= 3n ; n ϵ N ˄ n ≤ 3}

Hallar:

a. ( AᴜB )´∩ C
b. [( B∩C ) ᴜ A]- D´
c. ( B ΔC ) ∩ (A´Δ D)

Solución:
U = { 0,1,2,3,4,5,6,7,8,9,10}
A = {0,1,2,3}
B = {0,1,2,3}
C ={0,2,4,6,8,10}
D = {0,3,6,9}

a. (AUB)´∩ C
(AUB) = {0,1,2,3}
(AUB)´∩C = {4,5,6,7,8,9,10} ∩ {0,2,4,6,8,10}

(AUB)´∩ C = {4,6,8,10}

b. [(B∩C) U A ]- D´
[(B∩C) U A ]= {0,2} U {0,1,2,3}
[(B∩C) U A]= {0,1,2,3} D´= {1,2,4,5,7,8,10}
[(B∩C) U A ]- D´= {0,1,2,3} – {1,2,4,5,7,8,10}

[(B∩C) U A ]- D´ = {0,3}

c. ( B ΔC ) ∩ (A´Δ D)
(BΔC) = {1,4,6,8,10}A´= {4,5,6,7,8,9,10}
(A´Δ D) = {4,5,6,7,8,9,10} Δ {0,3,6,9}
(A´Δ D) = { 0,3,4,5,7,8,10}
( B ΔC ) ∩ (A´Δ D) = {1,4,6,8,10} ∩ {0,3,4,5,7,8,10}

( B ΔC ) ∩ (A´Δ D) ={4,8,10}

2. Dados los conjuntos A = { 2;4;5 } , B { x Z / 0 x 4 } , C = { x Z / -1 x 2 } , Hallar :

a. (A∩B) x (B∩A)
b. (AxA) ∩ (CxB)
Solución:
A ={2,4,5}
B = {0,1,2,3,4}
C = {-1,0,1,2}

a. (A∩B) x (B∩A)
(A∩B) x (B∩A) = {2,4} x {2,4}

(A∩B) x (B∩A) = {(2;2),(2;4),(4;2),(4;4)}

b. (AxA) ∩ (CxB)(AxA) = {2,4,5} x {2,4,5}
(CxB) = {-1,0,1,2} x {0,1,2,3,4}
(AxA) ∩ (CxB) = {(2;2),(2;4),(2;5), {(-1;0),(-1;1),(-1;2),(-1;3),(-1;4),(4;2),(4;4),(4;5), ∩ (0;0),(0;1),(0;2),(0;3),(0;4),
(5;2),(5;4),(5;5)} (1;0),(1;1),(1;2),(1;3),(1;4),(2;0),(2;1),(2;2),(2;3),(2;4)}

(AxA) ∩ (CxB) = { (2;2),(2;4)}

3. En un estudio de mercado se observa que cuando su producto se vende a S/. 80 por unidad se pueden vender...