If A,B,C be three sets such that `A cup B=A cupC and Acap B=AcapC,`then

Options

A. A=B
B. B=C
C. A=C
D. A=B=C

Answer

B

Explanation

we have ,
`Acup B=Acup C`
`implies (Acup B) cap C=(Acup C)cap C`
`implies (AcapC) cup (Bcap C)=C`
`implies (A capB)cup (Bcap C)=C[ :' Acap C=AcapB]. . .(i)`
Again ,
`Acup B=Acup C`
` implies (Acup B)cap B=(Acup C)capB`
`implies B=(AcapB)cup (BcapC)`
from (i) and (ii) , we get B=C.