Question

Consideram multimile: A={x∈R|-3<1-2x<11} si B={x∈R| 1/2≤x+2/6≤5/3}.
a) determinati A intersectat cu Z
b)scrieti multimile A si B sub forma de intervale
c) determinati A intersectat cu B

Answer 1

-3<1-2x<11 /-1
-4<-2x<10 /:(-2)
2<x<5 deci A={2<x<5}

1/2<\x+1/3<\5/3 /-1/3
1/2-1/3<\x<\4/3 amplificam pe 1/2 cu 3 si pe 1/3 cu 2
(3-2)/6<\x<\4/3
1/6<\x<\4/3 deci B={1/6<\x<\4/3}

a) AΠZ={3,4}
b) A=(2,5) si B=[1/6,4/3]
c) AΠB= multimea vida