Let E be a no empty set with card=n≥1 Find in term of n Σ_(A,B⊆E) Card(A−B)=Σ_(A,B⊆E) Card(A∩B)=(1/3)Σ


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Question Number 104850 by ~blr237~ last updated on 24/Jul/20

$L e t E b e a n o e m p t y s e t w i t h c a r d = n ⩾ 1$ $F i n d i n t e r m o f n \sum_{A, B \subseteq E} C a r d (A - B) = \sum_{A, B \subseteq E} C a r d (A \cap B) = \frac{1}{3} \sum_{A, B \subseteq E} C a r d (A \cup B) = n 4^{n - 1}$
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