First slide

Operations on Sets

Question

In statistical survey of 1003 families of Kolkata, it was found that 63 families has neither a radio nor a TV 794 families has a radio and I87 has TV. The number of families in that group having both a radio and a TV is

Easy

A

36
B

41
C

32
D

None of these

Solution

Let R be the set of families having a radio and Z be the set of families having a TV.
Then,
$n (R \cup T)$
= Number of families having at least one of the radio and TV
= 1003 - 63 = 940
$n (R) = 794 and n (T) = 187$
Let x be the number of families having both a radio and a TV.
Then number of families who have only Radio = 794 - x
Number of families who have only TV = 187 - x
From Venn diagram,
$794 - x + x + 187 - x = 940$
$\Rightarrow 981 - x = 940$
$∴ x = 981 - 940 = 41$
Hence, the required number of families having both a radio and a TV is 41.

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