Question

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

Answer 1

From the question, we have

$\epsilon =[26,27,28,29,30,31,32,33,34,35,35,37,38,39,40,41,42,43,4]$

$A=[26,28,30,32,34,36,38,40,42,44]$

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

$n(A-B)=[26,28,30,32,24,26,28,40,42,44]-[27,30,33,36,39,42]$

$=[26,28,32,34,38,40,44]$

Therefore, $n(A-B)=7$

$A^{\prime }=[27,29,31,33,35,37,39,41,43]$

$n(A^{\prime }\cap B)=[27,29,31,33,35,37,39,41,43]\cap [27,30,33,36,39,42]$

$\Rightarrow [27,33,39]$

$\Rightarrow n(A^{\prime }\cap B)=3$

Thus $n(A-B)\ne n(A^{\prime }\cap B)$