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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"B^prime`

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Given,
`U={1,2,3,4,5,6,7,8,9},A={2,4,6,8}` and `B={2,3,5,7}`
`(i)(AuuB)^'`
`=>U-(AuuB)`
`=>{1,2,3,4,5,6,7,8,9}-{2,3,4,5,6,7,8}`
`=>{1,9}`
and,`A^'nnB^'`
...
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Let U={1,2,3,4,5,6,7,8,9}A={1,2,4,6,8} and B={2,3,5,7} Verify that (i)(A uu B)'=A'nn B'ii)(A nn B)'=A'uu B'

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(a) If U= {1,2,3,……, 10} ,A = { 1,2,3,4,5}, B= {1,3,5,7,9} , C {2,4,8,10}, verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) (iii) A-B=AcapB^(c) (iv) Acap(BuuC)=(AcapB)uu(AcapC) . (b) If U={1,2,3,4,5,6,7,8,9}, A={2,4,6,8} and B= {2,3,5,7}. Veify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

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