Question

If n(U) = 50, n(A) = 38, n(B)=30 then the least value of n(A∩B) is​

Answer 1

hope u get ur answer......thq

Answer 2

Given,

$\[\begin{array}{l}n\left( U \right) = 50\\n\left( A \right) = 38\\n\left( B \right) = 30\end{array}\]$

Solution,

Know that $\[n\left( {A \cup B} \right) \le n\left( U \right)\]$. So,

$\[ \Rightarrow n\left( {A \cup B} \right) \le 50\]$

Therefore,

$\[\begin{array}{l} \Rightarrow n\left( {A \cup B} \right) \le 50\\ \Rightarrow n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right) \le 50\end{array}\]$

Apply values.

$\[\begin{array}{l} \Rightarrow 38 + 30 - n\left( {A \cap B} \right) \le 50\\ \Rightarrow 68 - n\left( {A \cap B} \right) \le 50\\ \Rightarrow n\left( {A \cap B} \right) \ge 68 - 50\\ \Rightarrow n\left( {A \cap B} \right) \ge 18\end{array}\]$

Hence, the least value of $\[n\left( {A \cap B} \right)\]$ is $\[18.\]$