Question

Question in fig ans it ​

Answer 1

★Answer :-

• n(A ∪ B) is 30 .
• n(A) is 20 .
• n(B) is 15 .

★Question :-

If n(A - B) = 15 , n(B - A) = 10 and n(A ∩ B) = 5 , find

(i.) n(A ∪ B)  (ii.) n(A)  (iii.) n(B) .

★Step - By - Step Explanation :-

★Given :-

• n(A - B) = 15 .
• n(B - A) = 10 .
• n(A ∩ B) = 5 .

★Solution :-

i.) n(A ∪ B)

We know , that n(A ∪ B) = n(A - B) + n(B - A) + n(A ∩ B)

n(A ∪ B) = 15 + 10 + 5 = 30 .

Therefore , n(A ∪ B) is 30.

ii.) n(A)

We know that n(A - B) = n(A) - n(A ∩ B)

15 = n(A) - 5

n(A) = 15 + 5 = 20

Therefore , n(A) is 20.

iii.) n(B)

We know that n(B - A) = n(B) - n(A ∩ B)

10 = n(B) - 5

n(B) = 10 + 5 = 15 .

Therefore , n(B) is 15.

Note :- A extra formula is added kindly check it .

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Answer 2

Given:

        n(A-B) = 15

        n(B-A) = 10

        n(A∩B) = 5

To Find:

1. n(A∪B)
2. n(A)
3. n(B)

Solution:

According to the question,

• n(A-B) means only A.

• n(B-A) means only B.

• And, n(A∩B) means both A and B.

For n(A∪B),

Since A∪B is the number of all the A and B there can not be any repetition.

So it can be calculated by adding the given values of only A, only B, and both A and B.

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

                                  = 15 + 10 + 5

                                  = 30

Hence the value of n(A∪B) is 30.

For n(A),

n(A-B) means only A as it is excluded by all the B's. So,

                      n(A - B) = n(A) - n(A ∩ B)  

                               15 = n(A) - 5

                            n(A) = 15 + 5

                            n(A) = 20

Hence the value of n(A) is 20.

For n(B),

n(B-A) means only B as it is excluded by all the A's. So,

                      n(B - A) = n(B) - n(A ∩ B)

                               10 = n(B) - 5

                            n(B) = 10 + 5

                            n(B) = 15

Hence the value of n(B) is 15.