Question

Se considera multimile: A={x|x=a/12( fractie) şi a|12
B={x|x=12/b ( fractie) şi b|12
C={x|x=a/b ( fractie) a|4 şi b|6
1. Enumerati elementele multimilor A, B, C
2. scrieți elementele reuniuni celor trei multimi

Answer 1

In multimea A :
a este divizor al lui 12 => a ∈ {1,2,3,4,6,12}
x = a/12 => x ∈ {1/12, 2/12, 3/12, 4/12, 6/12, 12/12} => x ∈ {1/12, 1/6, 1/4, 1/3, 1/2, 1} 
Deci A={1/12, 1/6, 1/4, 1/3, 1/2, 1} .

In multimea B :
b este divizor al lui 12 => b ∈ {1,2,3,4,6,12}
x=12/b => x ∈ {12/1, 12/2, 12/3, 12/4, 12/6, 12/12} => x ∈ {12, 6, 4, 3, 2, 1}
Deci B = {1,2,3,4,6,12}.

In multimea C :
a ∈ {1,2,4}
b ∈ {1,2,3,6}
c ∈ {1/1,1/2,1/3,1/6,  2/1,2/2,2/3,2/6,   4/1,4/2,4/3,4/6} - se vor elimina elementele egale => c ∈ {1/6,1/3,1/2,2/3,1,4/3,2,4}
Deci C = {1, 1/2, 1/3, 1/6, 2, 2/3, 4, 4/3} => C={1/6,1/3,1/2,2/3,1,4/3,2,4}

A U B U C = {1/12, 1/6, 1/4, 1/3, 1/2, 1} U  {1,2,3,4,6,12} U {1/6,1/3,1/2,2/3,1,4/3,2,4} = {1/12, 1/6, 1/4, 1/3, 1/2, 2/3, 1, 4/3, 2, 3, 4, 6, 12}