Question

Dados los intervalos: A = [-2, 4]; B = (-2, 4); C = ]-1, 4]; D = (-4, 6]. Determine gráfica y analíticamente:
a) A U B
b) A - B
c) B ∩ A
d) B c
e) A’

Answer 1

Respuesta:

a) A U B = [-2,-1,0,1,2,3,4]

b) A - B = [0]

c) B ∩ A =  [-2,-1,0,1,2,3,4]

d) B c = 128 subconjuntos

e) A’ = [-∞,...-3,5,..,∞]

Explicación paso a paso:

a) A U B = [-2,-1,0,1,2,3,4] U [-2,-1,0,1,2,3,4] = [-2,-1,0,1,2,3,4]

b) A - B = [-2,-1,0,1,2,3,4] - [-2,-1,0,1,2,3,4] = [0]

c) B ∩ A = [-2,-1,0,1,2,3,4] ∩ [-2,-1,0,1,2,3,4] =  [-2,-1,0,1,2,3,4]

d) B c = 2^7 = 128 subconjuntos

e) A’ = U-A

donde U es el universo, entonces

A’ = U-A = [-∞,∞] - [-2,-1,0,1,2,3,4] =  [-∞,...-3,5,..,∞]

Answer 2

Respuesta:

Dados los intervalos: A=[-2,4]; B=(-2,4); C=]-1,4]; D=(-4,6)

a) A U B = [-2, -1, 0, 1, 2, 3, 4]   R/.

b) A - B = [ 0 ]   R/.

c) B ∩ A =  [-2, -1, 0, 1, 2, 3, 4]   R/.

d) B^c = 2^7 = 128 subconjuntos   R/.

e) A' = [- ∞, ... -3,5 ..., ∞]   R/.

Explicación paso a paso:

Dados los intervalos: A=[-2,4]; B=(-2,4); C=]-1,4]; D=(-4,6)

      A = [-2, -1, 0, 1, 2, 3, 4]

     B = (-2, -1, 0, 1, 2, 3, 4)

a) A U B

    A U B = [-2, -1, 0, 1, 2, 3, 4] U (-2, -1, 0, 1, 2, 3, 4)

    A U B = [-2, -1, 0, 1, 2, 3, 4]   R/.

b) A - B

    A - B = [-2, -1, 0, 1, 2, 3, 4] - (-2, -1, 0, 1, 2, 3, 4)

    A - B = [ 0 ]   R/.

c) B ∩ A

    B ∩ A = [-2, -1, 0, 1, 2, 3, 4] ∩ [-2, -1, 0, 1, 2, 3, 4]

    B ∩ A =  [-2, -1, 0, 1, 2, 3, 4]   R/.

d) B^c

    B^c = 2^7 = 128 subconjuntos   R/.

e) A'

    A' = U-A U es el universo

    A' = [- ∞, ∞] - [-2, -1, 0, 1, 2, 3, 4]

    -2 -1 = - 3

    0, 1, 2, 3, 4 son de un intervalo cerrado = 5 elementos, tenemos,

    A' = [- ∞, ... -3,5 ..., ∞]   R/.