Question

Fie multimile : A= {x apartine Q | x=2 la puterea "a", -2 < a ≤ cu 1} si B {y apartine Q | y= 3 la puterea "b-3", 2 ≤ cu b < 5}. Determinati multimile:
A=
B=

A U B =
A - B=
A x B=
A ∩ B=
B - A=
B x A=

Answer 1

x= $2^{a}$
-2 < a ≤ 1 => a∈ {-1,0,1}
A= {$2^{-1} , 2^{0}=1 , 2^{1} =2$}

y= $3^{b-3}$
2 ≤ b < 5  | -3
-1≤ b-3 <2 => b-3 ∈ {-1,0,1}
B= {$3^{-1} , 3^{0} =1, 3^{1}=3$}

A U B = {$2^{-1} ,3^{-1} ,1, 2,3$}
A - B={$2^{-1} ,2$}
A x B={$( 2^{-1}, 3^{-1}),( 2^{-1},1 ),( 2^{-1} ,3),(1, 3^{-1} ),(1,1),(1,3),(2, 3^{-1} ),(2,1),(2,3)$}
A ∩ B= {1}
B - A={$3^{-1} ,3$}
B x A=$( 3^{-1},2^{-1}),(3^{-1},1 ),(3^{-1},2 ),( 1,2^{-1} ),(1,1),(1,2),( 3,2^{-1}),(3,1),(3,2)$