Question

Given, $\xi$ $=$ {Natural numbers between $25$ and $45$}; $A=$ {even numbers} and $B$ {multiples of $3$}. Find : $n(A$ ${}^{{}^{\prime }}$$\cap$ $B)$.

Answer 1

$\xi =$ { $26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44$ } as $x$ is a natural number between $25$ and $45$

$A=$ { $26,28,30,32,34,36,38,40,42,44$ } as $A$ is set of a multiple of $3$ within the limits of the universal set already defined as $\xi$

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

And, $B=$ { $27,30,33,36,39,42$ } as $B$ is a set of multiple of $3$ within the limits of the universal set already defined as $\xi$

Now, $A^{{}^{\prime }}\cap B=$ { $27,33,39$ }

$\Rightarrow n(A^{{}^{\prime }}\cap B)=3$ as there are $3$ elements in the Set $A^{{}^{\prime }}\cap B$