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Let"U"={1,2,3,4,5,6,7,8,9},A={2,4,6,8}a ...

Let`"U"={1,2,3,4,5,6,7,8,9},A={2,4,6,8}a n dB={2,3,5,7}dot` Verify that: `(AuuB)^'=A 'nnB '` (ii) `(AnnB)^'=A^(prime)uu"Bprime^"dot`

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(i) `A cup B={2,3,4,5,6,7,8}`
then, `(A cupB)'=U-(A cup B)`
`={1,9}`....(1)
Now, `A'=U-A={1,3,5,7,9}`
and `B'=U-B={1,4,6,8,9}`
`:. A' cap B' = {1,9}`...(2)
then from equations (1) and (2), `(A cupB)'=A'capB'`
(ii) `A cap B={2}`
then, `(A capB)'=U-(A capB)`
`rArr(A capB)'={1,3,4,5,6,7,8,9}` ....(3)
`A'= U-A={1,3,5,7,9}`
and `B' = U-B = {1,4,6,8,9}`
then, `A' cupB'={1,3,4,5,6,7,8,9}` ....(4)
Then it is clear from equations (3) and (4) that
`(A cap B)'=A' cup B'`.
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