If n(μ) = 60 , n(A) = 21, n(B) = 43 then Least value of n (A∩ B) and Greatest value of n (A∩ B) are

Question

If n(μ) = 60 , n(A) = 21, n(B) = 43 then Least value of n (A∩ B) and Greatest value of n (A∩ B) are (A) 2, 31 (B) 3, 36 (C) 1,24 (D) 4,21

Tardigrade Admin · Accepted Answer

n(μ) = 60, n(A) =21, n(B) =43 Greatest value of n(A∩ B) =n(A) =21 n(A∪ B) le60 ⇒ n(A) + n(B)-n(A∩ B) = 60 ⇒ n(A ∩ B) ge21 + 43 - 60 = 4 Least value of n(A ∩ B)=4

Q. If $n (μ) = 60$ , $n (A) = 21$ , $n (B) = 43$ then Least value of $n (A \cap B)$ and Greatest value of $n (A \cap B)$ are

2, 31

3, 36

1,24

4,21

$n (μ) = 60, n (A) = 21, n (B) = 43$
Greatest value of $n (A \cap B) = n (A) = 21$
$n (A \cup B) \leq 60$
$\Rightarrow n (A) + n (B) - n (A \cap B) = 60$
$\Rightarrow n (A \cap B) \geq 21 + 43 - 60 = 4$
Least value of $n (A \cap B) = 4$

Q. If n(μ)=60 , n(A)=21, n(B)=43 then Least value of n(A∩B) and Greatest value of n(A∩B) are