Let A and B be two sets such that the number of elements in A is 3 and the number of elements in B is 6. What is the minimum number of elements in the union of A and B?

B. 6 — The number of elements in the union is given by n(A union B) = n(A) + n(B) - n(A intersection B). To minimize the union, we must maximize the intersection, which occurs when A is a subset of B.

JEE Main · MathematicsMedium

$Let A and B be two sets such that n (A) = 3 and n (B) = 6 . What is the minimum number of elements in A \cup B ?$

A. $3$
B. $6$
C. $9$
D. $0$

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Correct answer: B — $6$

Solution

n (A \cup B) = n (A) + n (B) - n (A \cap B) . To minimize n (A \cup B), we maximize n (A \cap B), which is n (A) = 3 since A \subset B . Thus, $3 + 6 - 3 = 6$.

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Let A and B be two sets such that n(A)=3 and n(B)=6. What is the minimum number of elements in A∪B?

Solution

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More Sets & Relations practice questions

$Let A and B be two sets such that n (A) = 3 and n (B) = 6 . What is the minimum number of elements in A \cup B ?$