Question

n(B) =40 , n(A∩ B) =20, n( AU B)= 35, find n(A) *​

Answer 1

Answer:

∴ n(A) = 15

Step-by-step explanation:

Given,

  n(B) = 40

n(AnB) = 20

n(AUB) = 35

To find:

n(A) = ?

from formula,

    n(AUB) = n(A) + n(B) - n(AnB)

or, 35 = n(A) + 40 - 20

or, 35 = n(A) + 20

or, n(A) = 35 - 20

∴ n(A) = 15

   

Answer 2

Answer:

Required value of n(A) is 15.

Step-by-step explanation:

We know,$n(A) = n(A∩ B) + n( AU B) - n(B) ......(1)$

This is a problem of set theory.By equation number (1),we can find n(B),n(A∩ B),n(A),n( AU B) alternatively.

For example,

Let n(B) =20 , n(A∩ B) =10, n( AU B)= 25

then $n(A) = 10 + 25 - 20 = 15$

Here given,n(B) =40 , n(A∩ B) =20, n( AU B)= 35

From equation (1),

$n(A) = 20 + 35 - 40 = 15$

Required value of n(A) is 15.

Above formula only for 2 sets.

If there are three sets then $n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C).$