1. Tardigrade
  2. Question
  3. Mathematics
  4. If U be the universal set and A, B are subsets of U such that n(U) = 25, n(A) = 15, n(A ∪ B)' = 8, n(A ∩ B) = 6 then n(B) and n(B -A) are respectively given by the ordered pair

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Q. If $U$ be the universal set and $A$, $B$ are subsets of $U$ such that $n(U) = 25$, $n(A) = 15$, $n(A \cup B)' = 8$, $n(A \cap B) = 6$ then $n(B)$ and $n(B -A)$ are respectively given by the ordered pair

Sets

Solution:

$n(B - A) = n(U) - [n(A \cup B)' + n(A)]$
$= 25 - (8 + 15) = 2$
$\therefore n(B) = n(B - A) + n(A \cap B) = 2 + 6 = 8$
$\therefore $ Required ordered pair $= (8,2)$