Question

if n(A)=25
n(B)=40
n(AUB)=50
n(B') =25
Find n(A intersection B) and n (U)

any one pls answer the correct one ​

Answer 1

✿ Answer:

★ n(A∩B) = 15

★ n (U) = 65

✿ Step-by-step explanation:

Given:

• n (A) = 25
• n (B) = 40
• n (A ∪ B) = 50
• n (B') = 25

To find:

• n (A∩B) = ?
• n (U) = ?

Solution:

We know that:

n(A ∪ B) = n(A) + n(B) - n(A∩B)

→ 50 = 25 + 40 - n(A∩B)

→ 50 = 65 - n(A∩B)

→ 50 + n(A∩B) = 65

→ n(A∩B) = 65 - 50

→ n(A∩B) = 15

Also,

n (B') = n (U) - n (B)

→ 25 = n (U) - 40

→ n (U) = 40 + 25

→ n (U) = 65