In a statistical investigation of 1003 families of Calcutta, it was found that 63 families have neither a radio nor a TV, 794 families have a radio, and 187 have a TV. The number of families having both a radio and a TV is:
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Use set operations to solve logical counting problems.
Applying set theory principles:\[n(R) = 794, \quad n(T) = 187, \quad n(R \cup T)' = 63\]The total number of elements is the sum of elements in \(R \cup T\) and its complement \(R \cup T)'\). Therefore:\[n(Total) = n(R \cup T) + n(R \cup T)' \Rightarrow 1003 = n(R \cup T) + 63\]This yields:\[n(R \cup T) = 940\]Employing the principle of inclusion-exclusion:\[n(R \cup T) = n(R) + n(T) - n(R \cap T)\]Substituting the known values:\[940 = 794 + 187 - n(R \cap T)\]Solving for the intersection:\[n(R \cap T) = 41\]