Question

if n(AUB) = 10, n(B) = 7, n(A) = 5 Then n (A∩B) =
(A) 2
(B) 3
(C) 4
(D) 5​

Answer 1

Answer:

(A)2

Step-by-step explanation:

let n(A∩B)=x

n(AUB)=n(A) + n(B) - n(A∩B)

10=5+7-x

x=2

Answer 2

Given:

• n (AUB) = 10
• n (B) = 7
• n (A) = 5

To find:

• n (A∩B) = ?

Solution:

For solving such type of questions, we use the general formula of 2 events in sets.

n (AUB) = n (A) + n (B) - n (A∩B)

⇒ 10 = 5 + 7 - n (A∩B)

⇒ 10 = 12 - n (A∩B)

⇒ 10 + n (A∩B) = 12

⇒ n (A∩B) = 12 - 10

⇒ n (A∩B) = 2

∴ n (A∩B) = 2

Option (A) is correct.

KNOW MORE:

• De Morgan's law states that (A∩B)' = A' U B'