$A$ and $B$ are two finite sets such that $n (A) = m_{1}$ and $n (B) = m_{2}$ , then find the least and greatest values of $n (A \cup B)$ .

Open in App

Solution

$n (A \cup B) = n (A) + n (b) - n (A \cap B)$
Max Value $= m_{1} + m_{2}$ When $n (A \cap B) = 0$ that is there is no same element in A and B .
Assuming $m_{1} \geq m_{2}$
Min value $= m_{1}$ when $n (A \cap B) = m_{2}$
Assuming $m_{1} \leq m_{2}$
Min value $= m_{2}$ when $n (A \cap B) = m_{1}$

Suggest Corrections

Similar questions

A

B

n (A - B) = 30, n (A \cup B) = 180

n (B)

Let A and B be two finite disjoint sets such that n(A U B) = 475 and n(A) = 435, then n(B) is

n (A) = 17

n (B) = 29.

n ((A \cup B) - (A \cap B))

Join BYJU'S Learning Program