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

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Question: Answered & Verified by Expert

If

A

&

B

are two sets such that

n (A \times B) = 60

&

n (A) = 12

also

n (A \cap B) = K

, then the sum of maximum & minimum possible value of

K

is

MathematicsSets and RelationsJEE Main

Options:

A $17$
B $12$
C $5$
D $7$

Solution:

2356 Upvotes Verified Answer

The correct answer is:

5

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

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