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