Question

Dados los conjuntos A,B,C⊂R, con R={x∈Z|−20≤x≤20}, A={−9,−14,−6,−3,−11}, B={−11,1,4,7,−14}, y C={14,16,−6,19,6,−11} . El conjunto [(A△B)∖C]∪[(A∪B)c∩C] es:

Recuerda que A△B=(A∪B)∖(A∩B)

Seleccione una:
a. {-9, -14, -6,-3, 1, 4, 7, 14}
b. Ø
c. {-9, -14, -6,-3, 1, 4, 16, 19,6}
d. {-9, -3, 4,1, 7, 14, 16, 19,6}
e. {-11, 1, 4,7, 14, 16, 19,6, -6}

Ayuda por favor

Answer 1

Dados los conjuntos A, B y  C, El conjunto  [(A△B)∖C]∪[(A∪B)c∩C] es igual a {−9,−3,1,4,6,7,14,16,19}, la opción d es correcta.

Datos

A={−9,−14,−6,−3,−11}

B={−11,1,4,7,−14}

C={14,16,−6,19,6,−11}

R={-20,-19,-18,-17,-16,-15,-14,-13,-12,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,01,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

[(A△B)∖C]∪[(A∪B)∩C]

Resolver por parte

(A△B)∖C = ((A∪B)c∖(A∩B))∖C

A∪B = {−14,−11,−9,−6,−3,1,4,7}

A∩B ={−14,−11}

((A∪B)∖(A∩B))={−9,−6,−3,1,4,7}

((A∪B)∖(A∩B))∖C ={−9,−3,1,4,7}

(A△B)∖C ={−9,−3,1,4,7}

(A∪B)c={-20,-19,-18,-17,-16,-15,-13,-12,-10,-8,-7,-5,-4,-2,-1,0,2,3,5,6,8,9,10,11,12,13,14,15,16,17,18,19,20}

(A∪B)∩C= {6,14,16,19}

[(A△B)∖C]∪[(A∪B)∩C] ={−9,−3,1,4,6,7,14,16,19}