Question

Q. If n(U) = 14, n(A) = 7, n(B) = 5 and n(AnB) = 2, then n(A'nB') = ?
(step-wise explanation) ​

Answer 1

Answer:

$\tiny \tt \: If \: \: \: n( \cup) = 14, n(A) = 7, n(B) = 5 \: \: \: and \: \\ \tt \tiny\: n(A \cap B) = 2, then \: \: \: n(A' \cap B') =$

Step-by-step explanation:

Given: n(A)=7, n(B)=5 and $\tt n(A \cap B)=2$

To Find: $\tt n\left(A^{\prime} \cap B^{\prime}\right) \quad n(\cup)=14$

Solution:

$\color{maroon}\[ \begin{aligned} & \tt n(A \cap B)=2 \\ \\ \therefore \: \: \: \: \: & \tt n(A \cap B)=n(A)+n(B)-n(A \cap B) \\ \\ \therefore \: \: \: \: \: & \tt n(A \cap B)=7+5-2=10 \text { Now } \\ \\ & \tt n\left(A {}^{ \prime} \cap B^{\prime}\right)=n( \cup)-n(A \cup B) \\ \\ & \tt=14-10 \\ \\ & \tt = 4\end{aligned} \]$