Question

Daca A,B si C subt 3 multimi avand card AxB= 77, card BxC=91 si card AxC=143, determina card C.
URGEENT

Answer 1

Știm că: $\text{card}(A \times B) = \text{card}(A) \cdot \text{card}(B)$.=

$\text{card}(A \times B) = 7 \cdot 11 = 11 \cdot 7.\\\text{Daca \text{card}(B) = 11 } \implies 11 \vert 91 \text{, ceea ce e fals, deci \text{card}(A) = 11 }\\\text{card}(C) = \frac{143}{\text{card}(A)} = \frac{143}{11} = \boxed{13}$