Question

Given, $\xi$ $=$ {Natural numbers between $25$ and $45$}; $A=$ {even numbers} and $B$ {multiples of $3$} then $n\left(A\right)+n\left(B\right)=n(A$ $\cup$$B)+n(A$ $\cap$ $B$) .If true enter 1 else 0.

Answer 1

From the given sets, we have

$\epsilon =[26,27,28,29,30,31,32,33,34,35,35,37,38,39,40,41,42,43,44]$

$A=[26,28,30,32,24,26,38,40,42,44]$

$B=[27,30,33,36,39,42]$

$n\left(A\right)=10$ and $n\left(B\right)=6$

$\therefore n\left(A\right)+n\left(B\right)=10+6=16$

We know that

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow n(A\cup B)+n(A\cap B)=n\left(A\right)+n\left(B\right)$

$\Rightarrow n(A\cup B)+n(A\cap B)=16$

Therefore, $n\left(A\right)+n\left(B\right)=n(A\cup B)+n(A\cap B)$