Question

In the given Venn-diagram, if n(AUB) = 50, find n (A).

n°(A) = 2a
n°(B)=a
n(A[intersection]B)=20​

Answer 1

n(A U B) = n(A) + n(B) – n(A ∩ B)

putting values we get

50 = 2a + a - 20

solving eqn.

70 = 3a

a = 70 / 3

now n(a) = 2a

= 2 x 70/3

= 140/3

hence, n(a) = 140/3

Answer 2

We can use the formula:

n(A U B) = n(A) + n(B) - n(A [intersection] B)

Substituting the given values, we get:

50 = 2a + a - 20

Simplifying and solving for a, we get:

a = 35

Therefore, n(A) = 2a = 2(35) = 70.

So, the value of n(A) is 70.