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fie M si N doua multimi. Daca card M * card (M minus N) = 15, determinati card (M intersectat N).

Răspuns :

Desenam diagrama Venn.

Notam : 

[tex]card(M)=x, \ \ card(M\cap N)=y[/tex]

Avem :

[tex]card(M)\cdot card(M-N) = card(M)\cdot [card(M)-card(M\cap N)]= \\\;\\ =x(x-y)=15 \Longrightarrow \begin{cases} x(x-y) = 15\cdot1\\\;\\ x(x-y) = 5\cdot 3\end{cases} [/tex]