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The value of (A cup B cup C) cap (A cap ...

The value of `(A cup B cup C) cap (A cap B^(C)capC^(C)) cap C^(C)` is

A

`B cap C'`

B

`B'cap C'`

C

`B capC`

D

`A cap B cap C`

Text Solution

Verified by Experts

we have ,
`(A' cup B' cup C')=A'cup Bcup C`
`therefore (Acup BcupC)cap (Acap B'cap C') '`
`= (A cup B cup C)cap (A' cup Bcup C)`
`=(Acap A')cup (Bcup C)`[ by distributivity of `cup" over" cap`]
`= phi cup (B cup C) =Bcup c`
hence ,
`(Acup Bcup C)cap (AcapB'cap C)cap C'
=(B cap C)cap c' =(B cap c') cup (CcapC')=BcapC'`
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OBJECTIVE RD SHARMA ENGLISH-SETS-Section I - Solved Mcqs
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  3. Let A and B be two sets that Acap X =Bcap X=phi and Acup X=Bcup X ...

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  12. If A={x,y):x^(2)+y^(2)=25} and B={(x,y):x^(2)+9y^(2)=144}, then A ...

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  13. If n(A) = 10,n(B) = 6 and n( C ) =5 for three disjoint sets A,B...

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