If A and B are two sets such that n(A × B)=60 , n(A)=12 and n(A ∩ B)=K , then the sum of maximum and minimum possible value of K is

Question

If A and B are two sets such that n(A × B)=60 , n(A)=12 and n(A ∩ B)=K , then the sum of maximum and minimum possible value of K is (A) 17 (B) 12 (C) 5 (D) 7

Tardigrade Admin · Accepted Answer

n(B)=(n (A × B)/n (A))=5 ∴ n(A ∩ B) has minimum value =0 and n(A ∩ B) has maximum value =n(B)=5

Q. If $A$ and $B$ are two sets such that $n (A \times B) = 60$ , $n (A) = 12$ and $n (A \cap B) = K$ , then the sum of maximum and minimum possible value of $K$ is

$17$

$12$

$5$

$7$

$n (B) = \frac{n ( A \times B )}{n ( A )} = 5$
$∴$ $n (A \cap B)$ has minimum value $= 0$
and $n (A \cap B)$ has maximum value $= n (B) = 5$

Q. If A and B are two sets such that n(A×B)=60 , n(A)=12 and n(A∩B)=K , then the sum of maximum and minimum possible value of K is

17

12

5

7

n(B)=n(A)n(A×B)​=5 ∴ n(A∩B) has minimum value =0 and n(A∩B) has maximum value =n(B)=5

Q. If $A$ and $B$ are two sets such that $n (A \times B) = 60$ , $n (A) = 12$ and $n (A \cap B) = K$ , then the sum of maximum and minimum possible value of $K$ is

$17$

$12$

$5$

$7$

$n (B) = \frac{n ( A \times B )}{n ( A )} = 5$
$∴$ $n (A \cap B)$ has minimum value $= 0$
and $n (A \cap B)$ has maximum value $= n (B) = 5$