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

Options

A. `B cap C'`
B. `B'cap C'`
C. `B capC`
D. `A cap B cap C`

Explanation

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'`