Question

Cunoscand card A = 5 , card B = 8 iar card ( A ∪ B ) = 10 , aflati card ( A ∩ B )

Answer 1

$\displaystyle Notez~ |X|=cardX. \\ \\ Din~identitatea~|A \cap B|=|A|+|B|-|A \cup B| ~rezulta: \\ \\ |A \cap B|=5+8-10=3. \\ \\ card(A \cap B)=3.$

Answer 2

card(AUB) =cardA + cardB - card(A∩ B) ⇒ 10 = 5+8 -card(A∩ B) ⇒

⇒ card(A∩ B)  = 5+8-10 ⇒ card(A∩ B)  = 3.