मान लीजिए कि `U={1,2,3,4,5,6,7,8.9},A={1,2,3,4},B={2,4,6,8}` और `C={3,4,5,6}` तो निम्नलिखित ज्ञात कीजिएः
(i) `A’` (ii) `B’`
(iii) `(AuuC)’` (iv) `(AuuB)’`
(v) `(A’)’` (vi) `(B-C)’`

Explanation

(i) `U={1,2,3,4,5,6,7,8,9}` तथा `A={1,2,3,4}`
तब `A` का पूरक समुच्य्, `A’=U-A`
`={5,6,7,8,9}`
अतः `A’={5,6,7,8,9}`
(ii) `U={1,2,3,4,5,6,7,8,9}` तथा `B={2,4,6,8}`
तब `B` का पूरक समुच्चय `B’=U-B`
`={1,3,5,7,9}`
अतः`B’={1,3,5,7,9}`
(iii) `U={1,2,3,4,5,6,7,8,9},A={1,2,3,4}`
तथा `C={3,4,5,6}`
तब `AuuC={1,2,3,4,5,6}`
`:.(AuuC)’=U-(AuuC)`
`={7,8,9}`
अतः `(AuuC)’={7,8,9}`
(iv) `U={1,1,3,4,5,6,7,8,9},A={1,2,3,4}` तथा `B={2,4,6,8}`
तब `AuuB={1,2,3,4,6,8}`
`:.(AuuB)’=U-(AuuB)`
`={5,7,9}`
अतः `(AuuB)’={5,7,9}`
(v) `U={1,2,3,4,5,6,7,8,9}` तथा `A={1,2,3,4}`
`:.A’=U-A={5,6,7,8,9}`
तथा `(A’)’=U-A’`
`={1,2,3,4}=A`
`(A’)’={1,2,3,4}`
(vi) `U={1,2,3,4,5,6,7,8,9},B={2,4,6,8}` तथा `C={3,4,5,6}`
तब `B-C={2,8}`
`:.(B-C)’=U-(B-C)`
`={1,3,4,5,6,7,9}`
अतः `(B-C)’={1,3,4,5,6,7,9}`