Question

Sendo A = {x ∈ N : x^ − 4 = 0}, B = {x ∈ Z : −2 ≤ x < 5} e C = {x ∈ Z : 0 < −3x+2 ≤ 5}.
3
Determinar:
a) A ∩ B
b) B ∩ C
c) A ∪ (B ∩ C)
d) A ∩ B ∩ C
e) A ∪ B ∪ C

Answer 1

A = {x ∈ N : x^2 − 4 = 0}

A = {2}

B = {x ∈ Z : −2 ≤ x < 5}

B = {-2,-1,0,1,2,3,4}

C = {x ∈ Z : 0 < −3x+2 ≤ 5}

C = {-1,0}

a) A ∩ B

{2} ∩ {-2,-1,0,1,2,3,4} = {2}

b) B ∩ C

{-2,-1,0,1,2,3,4} ∩ {-1,0} = {-1,0}

c) A ∪ (B ∩ C)

{2} ∪ ({-1,0})

{2} ∪ {-1,0} = {-1,0,2}

d) A ∩ B ∩ C

{2} ∩ {-2,-1,0,1,2,3,4} ∩ {-1,0} = { }

e) A ∪ B ∪ C

{2} ∪ {-2,-1,0,1,2,3,4} ∪ {-1,0} =

={-2,-1,0,1,2,3,4}