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Let-E-be-a-no-empty-set-with-card-n-1-Find-in-term-of-n-A-B-E-Card-A-B-A-B-E-Card-A-B-1-3-A-B-E-Card-A-B-n4-n-1-




Question Number 104850 by ~blr237~ last updated on 24/Jul/20
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_(A,B⊆E) Card (A∪B)=n4^(n−1)
$${Let}\:\:{E}\:{be}\:{a}\:{no}\:{empty}\:{set}\:{with}\:{card}={n}\geqslant\mathrm{1} \\ $$$$\:{Find}\:{in}\:{term}\:{of}\:\:{n}\:\:\:\:\:\:\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}−{B}\right)=\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}\cap{B}\right)=\frac{\mathrm{1}}{\mathrm{3}}\underset{{A},{B}\subseteq{E}} {\sum}{Card}\:\left({A}\cup{B}\right)={n}\mathrm{4}^{{n}−\mathrm{1}} \:\:\:\: \\ $$

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