If n(A ∩ B) = 10, n(B ∩ C) = 20 and n(A ∩ C) = 30, then the greatest possible value of n(A ∩ B ∩ C) is ____________.

Open in App

Solution

If n(A ∩ B) = 10
n(B ∩ C) = 20
n(A ∩ C) = 30
To find the greatest possible value of n(A ∩ B ∩ C)
Since A ∩ B ∩ C ≤ A ∩ B , A ∩ B ∩ C ≤ A ∩ C and A ∩ B ∩ C ≤ B ∩ C
⇒ n(A ∩ B ∩ C) ≤ n(A ∩ B), n(A ∩ B ∩ C) ≤ n(A ∩ C) and n(A ∩ B ∩ C) ≤ n(B ∩ C)
⇒ n(A ∩ B ∩ C) ≤ min{n(A ∩ B), n(A ∩ C), n(B ∩ C)}
≤ min {10, 20, 30} = 10
i.e maximum / greatest possible value of n(A ∩ B ∩ C) is 10.

Suggest Corrections

Similar questions

A, B, C

n (A) = 10, n (B) = 15, n (C) = 20, n (A \cap B) = 8

n (B \cap C) = 9

n (A \cup B \cup C)

n (A \cap B) = 3, n (B \cap C) = 6, n (A \cap C) = 5 a n d n (A \cap B \cap C) = 2

n [A \cup B \cup C] =

n (A) = 20, n (B) = 30

n (A \cup B) = 40

n (A \cap B)

A, B, C

U

n (U) = 692

n (B) = 230

n (C) = 370

n (B \cap C) = 20

n (A \cap B^{'} \cap C^{'}) = 10

n (A \cap B^{'} \cap C^{'})

Join BYJU'S Learning Program