$6.($a$)$ Let X UY $=$ X for any set X$.$ Prove that Y $=0.($b$)$ Let XnY $=$ X for any set X$.$ Prove that Y $=$ U$.7.8.$ Prove that AUB $=$ An Biff A $=$ B Prove that $9.($a$)$ An $($B $-$ A$)=0.(6)$ AU$($B $-$ A$)=$ AUB. $($C$)($AUB$)-$ C $=($A $-$C$)$ U $($B$-$C$).($d$)($A $-$ B$)$ U $($B $-$ A$)=($AUB$)-($ANB$).($e$)($A $-$ B $-$ C $=($A $-$C$)-($B$-$C$).$ Let A$,$ B$,$ C be sets. Prove that: $($a$)$ A CB iff AnB $=0.($b$)$ A C VD$14$ Biff $$UB $=$ U$.($c$)$ A $$ Biff $($ANB$).($d$)$ A $$ B iff $($ANB$)$ SB$.$