Question

For any two finite sets A and B. Which of the following is/are true?

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

Answer 1

Answer: (A), (C)

The correct options are
A $n\left(A\right)=n(A-B)+n(A\cap B)$
C $n\left(A\right)=n(A\cup B)-n(B-A)$

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

Number of elements in A is equal to number of elements only in A plus number elements in both A and B.

$n\left(A\right)=n(A\cup B)-n(B-A)$

Number of elements of set is equal A is equal to difference of number of elements in set A or B and number elements only in B