First slide

Operations on Sets

Question

A survey shows that 63% of the people watch a news channel whereas, 76% watch an entertainment channel at a particular time. lf x% of the people watch both types of
channels, then

Moderate

A

$x = 35$
B

$x \geq 63$
C

$39 \leq x \leq 63$
D

$x = 39$

Solution

Let A be the set of those people who watch news channel and
B be the set of those people who watch entertainment channel.
Then
$n (A) = 63, n (B) = 76, and n (A \cap B) = x$
$\begin{array}{l} ∵ n (A \cup B) \leq 100 \\ \Rightarrow n (A) + n (B) - n (A \cap B) \leq 100 \\ \Rightarrow 63 + 76 - x \leq 100 \\ \Rightarrow x \geq 39 \end{array}$
Also, $n (A \cap B) \leq min \cdot {n (A), n (B)}$
$\begin{array}{ll} \Rightarrow x \leq 63 \\ ∴ 39 \leq x \leq 63 \end{array}$

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