Question

$A=x/x$ is a two digit number, which divisible by $2$ (or) $3$ and $x\le 50$,$B=x/x$ is a two digit number, which divisible by $6$ and $x\le 50$.Find

1. $n(A\cup B)=$?
   
2. $n(A\cap B)=$?

Answer 1

$A=x:x$ is a two no. which is divisible by $2$ or $3$ and $x\le 50$

Such no. are $10,12,14,,15,16,.....,50$

Total Such no. are $n\left(A\right)=27$

$B=x:x$ is a two no. which is divisible by $6$

Such no. are $12,18,,24,36,.....,48$

Total Such no. are $n\left(B\right)=7$

No. divisible by $2$ or $3$ and $6$ $n(A\cap B)=7$

$n(A\cup B)=n\left(A\right)+n\left(B\right)+n(A\cap B)=27+7-7=27$