Question

Determinati multimile:
B={x apartine N/ 10/x-3 apartine Z}
C={x apartine Z_/3/x-1 apartine Z}
D={x aparține Z/ -5/ 4-x aparține N}

Answer 1

10/(x-3) ∈ Z ⇔ (x-3)∈ D10 ⇒ ( x -3) ∈ {-10, -5, -2, -1, 1, 2, 5 ,10}
x ∈{-7, - 2, 1, 2, 4, 5, 8, 13}    B = {1, 2, 4, 5, 8, 13} 
3/(x-1) ∈ Z  ⇔   (x - 1) ∈ D3    x ≠1     (x-1) ∈ {-3, -1, 3}    x ∈ {-2, 0, 4}
C = {-2} 
-5/(4 -x) = 5/(x-4) ∈ N ⇔  (x-4) ∈D5      (x - 4) ∈ { 1, 5}    x∈ { 5, 9}
D = {5,9}