Question

Fie multimile: A={x apartine Z | 7/2x+1 apartine Z} si B={ x apartine Z | 9/2x-3 apartine Z}
Calculaţi:
A; B; A reunit cu B; A intersectat cu B.
Dau coroana, pls

Answer 1

A= { x∈Z | 7/2x+1 } ∈ Z
B= { x∈Z | 9/2x- 3 } ∈ Z

D(7) = 1 ; 7 , -1 ; -7
2x+1=1     
2x=1-1
x=0/2
x=0         

2x+1=7
2x=7-1
x=6/2
x=3

2x+1=-1
2x=-1-1
x=-2/2
x=-1

2x+1=-7
2x=-7-1
x=-8/2
x=-4

A={0 ; 3 ; -1 ; -4}

D(9) = 1 ; 3 ; 9 ; -1 ; -3 ; -9
2x-3=1
2x=1+3
x=4/2
x=2

2x-3=3
2x=3+3
x=6/2
x=3

2x-3=9
2x=9+3
x=12/2
x=6

2x-3=-1
2x=-1+3
x=2/2
x=1

2x-3=-3
2x=-3+3
x=0/2
x=0

2x-3=-9
2x=-9+3
x=-6/2
x=-3

B={2;3;6;1;0;-3)

A∪B= {0; 3;-1;-4 ;2;3;6;1;0;-3 }
A∩B={0}