Question

determinați elementele următoarelor mulțimi :A={x€Z | 6 supra 2x +1€z} B={x€Z| -8 supra 3x - 1 C ={x€Z |4x - 2 supra 5x+1 €Z} D ={x € Z| 3x+4 supra 12 x-1 €N

Answer 1

46/(2x+1) ∈ Z  ⇔ (2x +1) ∈ D6      (2x+1)∈{-6,-3,-2,-1,1,2,3,6}
2x ∈ {-7,- 4,-3,-2,0,1,2,5}      A = {-2,-1,0,1}   
-8/(3x- 1) ∈Z ⇔ (1 - 3x) ∈ D(8)      (1-3x) ∈ {-8,-4,-2,-1,1,2,4,8}
-3x ∈ {-9,-5,-3,-2,0,1,3,7}      B = {3,1,0,-1} 
(4x-2)/(5x+1) ∈ Z ⇔ (5x+1) | (4x-2)
(5x+1) | (5x+1) ⇒ (5x+1) | 4(5x+1) = 20x + 4    (1)
(5x+1) | (4x-2) ⇒ (5x+1) | 5(4x-2) = 20x - 10     (2)
⇒ (5x+1) | [(1) - (2)] = 14 ⇒  (5x +1) ∈ {-14,-7,-2,-1,1,2,7,14}
5x ∈{-15,-8,-3,-2,0,1,6,13}    C = {-3,0} 
(3x+4)/(12x-1) ∈ N ⇔ (12x - 1) | ((3x+4)                
(12x-1) | (3x+4) ⇒ (12x-1) | 4(3x +4) = 12x + 16    (1)
(12x-1) |  (12x-1)    (2)
⇒ (12x-1) | [(1) - (2)] = 17    12x - 1 ∈ {-7,-1,1,17}    12x ∈ {-6,0,2,18} D={0}