यदि `U={1,2,3,4,5,6,7,8,9},A={2,4,6,8,}` तथा `B={2,3,5,7}` तो सत्यापित कीजिए-
(i) `(AuuB)'=A'nnB' " " (ii) (AuuB)'=A'uuB'`

Explanation

(i) `AuuB={2,4,6,8},uu{,23,5,7}={2,3,4,5,6,7,8}`
बायाँ पक्ष `=(AuuB)'=U-(AuuB)'={1,9}`
अब `A'=U-A={1,2,3,4,5,6,7,8,9,}-{{2,4,6,8}={1,3,5,7,9}`
व `B'=U-B={1,2,3,4,5,6,7,8,9}-{2,3,5,7}={1,4,6,8,9}`
दायाँ पक्ष `=A'uuB'={1,3,5,7,9}nn{1,4,6,8,9}={1,9}`
`:. (AuuB')=A'nnB'`
(ii) `AnnB={2,4,6,8,}nn{2,3,5,7}={2}`
`:. (AuuB)'={1,3,5,7,9,}uu{1,4,6,8,9}={1,3,4,5,6,7,8,9}`
`:. (AnnB)'=A'uuB'`