Question

1.Enumerati elementele multimilor:
    A= {x | x ∈ Z, x | -12};
    B= {x|x ∈ Z, -5|x si -32 ≤ x ≤ 42};
    C= {x|x ∈ Z, -205 / x};
    D= { x|x ∈ Z, x este multiplu de -3 si |x| ≤ 45}.

2. Fie a ∈ Z* si x ∈ Z+. Aratati ca urmatoarele propozitii sunt false:
p: a| x·y ⇒ a|x si a | y;
q: a| x·y ⇒ a | x sau a | y.

Answer 1

daca A={x|x∈Z, x |-12}   atunci :A={-12,-6,-4,-3,-2,-1,1,2,3,4,6,12}
B={x|x∈Z, -5|x si -32≤x≤42}  =>B={-30,-25,-20,-15,-10,-5,5,10,15,20,25,30,35,40}
C={x| x∈Z, -205|x} Conform definitiei, cum ca  a|b daca exista un numar c astfel incat b=a*c=> C={-205,-410,-605..., 205,410,605,....,k*205}k∈Z
D= {x | x∈Z, x este multiplu de -3 si |x|≤45} D={45,42,39,36,33,30,27,24,21,18,15,12,9,6,3,-3,-6,-9,-12,-15,-18,-21,-24,-27,-30,-33,-36,-39,-42,-45}