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) $