Question

If n(AnB) = 36,n (A – B) = 25, n(B - A) = 20 then find the value of n(AUB), n(A)and n (B)​

Answer 1

Given:

n(A n B) = 36

n(A – B) = 25

n(B - A) = 20

To Find:

(a) n (A U B)

(b) n (A)

(c) n (B)

Explanation:

n(A n B) = 36

There are 36 elements in both A and B

n(A – B) = 25

There are 25 elements that are in A but not in B

n(B - A) = 20

There are 20 elements that are in B but not in A

Solution

n (A U B) = In Both + In A but not in B + In B but not in A

n (A U B) = n(A n B) + n(A – B) + n(B - A)

n (A U B) = 36 + 25 + 20

n (A U B) = 81

n(A) =  In Both + In A but not in B

n(A)= n(A n B) + n(A – B)

n(A) = 36 + 25

n(A) = 61

n(B) =  In Both + In B but not in A

n(B) = n(A n B) + n(B - A)

n(B) = 36 + 20

n(B) = 56

Answer: (i) n(AUB) = 81     (ii) n(A) = 61       (iii) n(B) = 56

Answer 2

Answer:

n(AUB)=n(AnB)+n(A-B)+n(B-A)

=36+25+20

=81

n(A)=n(AnB)+n(A-B)

=36+25

=61

n(B)=n(A+B)+n(B-A)

=36+20

=56