Question

If $n(A)=$ number of elements in $A=n(B)$ then

• A. $n(A\sim B)=n(B\sim A)$
• B. $n(A\cup B)=n(A)+n(B)$
• C. $n(A\cap B)=n(B)+n(A\sim B)$
• D. None of these

Answer 1

Answer: (A)

Since, $A=\left(A-B\right)\cup \left(A\cap B\right)$
So, $n\left(A\right)=n\left(A-B\right)+n\left(A\cap B\right)....(1)$
Also, $B=\left(B\sim A\right)\cup \left(B\cap A\right)$
So, $n\left(B\right)=n\left(B\sim A\right)+n\left(A\cap B\right).....\left(2\right)$
Hence , if $n\left(A\right)=n\left(B\right)$ , then
$n\left(A-B\right)=n\left(B-A\right)$ {(using (1) & (2)}
Also, from (1) & (2), we have
$n\left(A\cap B\right)=n\left(A\right)-n\left(A\sim B\right)$
and $n\left(A\cap B\right)=n\left(B\right)-n\left(A\sim B\right)$