Question

fie multimea A={x∈Z║$\frac{9}{X-3}$∈Z SI B={X∈Z║6 DIVIDE X SAU 4DIVIDE X}
Determinati cele doua multimi si calculati A∩B

Answer 1

9/(x-3)∈Z ⇒ x-3 | 9 ⇒ x-3 ∈ {-9,-3,-1,1,3,9}  x≠3 (sa aiba sens fractia)

deci x∈{-6,0,2,4,6,12}=A
B={..-8,-6,-4,0,4,6,8,12,16,...}

A∩B = numerele din A divizibile cu 4 sau 6 deci A∩B= {-6,0,4,6,12}