First slide

Operations on Sets

Question

In a statistical investigation of 1003 families of Calcutta, it was found that 63 families has neither a radio nor a T.V, 794 families has a radio and 187 has T.V. The number of families in that group having both a radio and a T.V is

Easy

A

36
B

41
C

32
D

None of these

Solution

Let R be the set of families having a radio and T be the set of families having a T.V.,
then $n (R \cup T)$ = The number of families having at least one of the radio and T.V. = 1003 - 63 = 940
$n (R) = 794 and n (T) = 187$
Let x families have both a radio and a T.V. Then number of families who have only radio = 794 - x
And the number of families who have only T.V. = 187 - x
$From Venn diagram, 794 - x + x - 187 - x = 940$
Hence, the required number of families having both a radio and a T.V. =41

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