Question

Stabiliti cardinalul fiecarie dintre urmatoarele multimi. 

1. {x apartine Z | -10 < x }
2. {x apartine Z | -6 < x - 2}
3. {x apartine Z | |x| <sau egal 3}  
4. {x apartine Z | |x-2|<3}
Multumesc.

Answer 1

1. x > -10  ⇒ x = {-9;-8;-7;...;0;1;2;3;...; +∞} ⇔ x∈(-1; +∞) n Z;
2. -6<x<-2 ⇒ x ∈ (-6;-2) n Z;
3. |x| < 3    ⇒ -3 < x < 3 ⇔ x ∈ (-3;+3) n Z;
4. |x-2|<3 ⇔ -3<x-2<3 ⇔ -3+2<x<3-2 ⇔-1<x<1 ⇒ x∈(-1;+1) n Z;