1. Tardigrade
  2. Question
  3. Mathematics
  4. Let U be a Universal set and n(U)=12. If A, B ⊆ U are such that n(B)=6 and n(A ∩ B)=2 then n(A ∪ B prime) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $U$ be a Universal set and $n(U)=12$. If $A, B \subseteq U$ are such that $n(B)=6$ and $n(A \cap B)=2$ then $n\left(A \cup B^{\prime}\right)$ is equal to

Sets

Solution:

$n\left(A \cup B^{\prime}\right)=n(A)+n\left(B^{\prime}\right)-n\left(A \cap B^{\prime}\right) $
$=n(A)+n(U)-n(B)-(n(A)-n(A \cap B))$
$=n(U)-n(B)+n(A \cap B) $
$=12-6+2=8$