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1.Set Theory
medium
If $n(U)$ = $600$ , $n(A)$ = $100$ , $n(B)$ = $200$ and $n(A \cap B )$ = $50$, then $n(\bar A \cap \bar B )$ is
($U$ is universal set and $A$ and $B$ are subsets of $U$)
A
$300$
B
$350$
C
$250$
D
$200$
Solution
$\mathrm{n}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})=\mathrm{n}(\overline{\mathrm{A} \cup \mathrm{B}})$
$=\mathrm{n}(\mathrm{u})-\mathrm{n}(\mathrm{A} \cup \mathrm{B})$
$=600-(\mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})-\mathrm{n}(\mathrm{A} \cap \mathrm{B}))$
$=600-100-200+50=350$
Standard 11
Mathematics
