First slide

Operations on Sets

Question

A survey shows that 63% of the people watch a news channel whereas 76% watch another TV channel. If x% of the people watch both the channels, then

Moderate

A

x=35
B

x=63
C

$39 \leq x \leq 63$
D

x=39

Solution

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

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