Question

Seja os conjuntos X= {3,6,9,14,18,20}, Y= {x/x e Múltiplo positivos de 3} e Z= {x/x e divisor positivo de 12} determine: a. X-Yb. X-Zc. Z-Yd. (X∪Z)-Ye. Z-(Y∩X)f. (Z∩Y) - (X∩Z)

Answer 1

X = {3, 6, 9, 14, 18, 20}
Y = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30...}
Z = {1, 2, 3, 4, 6, 12}

a)
X - Y = {14, 20}

b)
X - Z = {9, 14, 18, 20}

c)
Z - Y = {1, 2, 4}

d)
(X ∪ Z) = {3, 6, 9, 14, 18, 20, 1, 2, 4}

e)
Z - (Y ∩ X) = {1, 2, 4, 12}

f)
(Z ∩ Y) - (X ∩ Z) = {12}

Answer 2

a. X - Y = {14, 20}

b. X - Z = {9, 14, 18, 20}

c. Z - Y = {1, 2, 4}

d. (X ∪ Z) - Y = {1, 2, 4, 14, 20}

e. Z - (Y ∩ X) = {1, 2, 4, 12}

f. (Z∩Y) - (X∩Z) = {12}

Explicação:

X = {3, 6, 9, 14, 18, 20}

Y = {x/x e múltiplos positivos de 3} Logo:

Y = {0, 3, 6, 9, 12, 15, 18...}

Z = {x/x e divisores positivos de 12} Logo:

Z = {1, 2, 3, 4, 6, 12}

a. X - Y = {3, 6, 9, 14, 18, 20} - {0, 3, 6, 9, 12, 15, 18...} = {14, 20}

b. X - Z = {3, 6, 9, 14, 18, 20} - {1, 2, 3, 4, 6, 12} = {9, 14, 18, 20}

c. Z - Y = {1, 2, 3, 4, 6, 12.} - {0, 3, 6, 9, 12, 15, 18...} = {1, 2, 4}

d. (X ∪ Z) - Y =

{1, 2, 3, 4, 6, 9, 12 14, 18, 20} - {0, 3, 6, 9, 12, 15, 18...} = {1, 2, 4, 14, 20}

e. Z - (Y ∩ X) =

{1, 2, 3, 4, 6, 12} - {3, 6, 9, 18} = {1, 2, 4, 12}

f. (Z∩Y) - (X∩Z) =

{3, 6, 12} - {3, 6} = {12}

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