In a survey of 100 households in Abuja, 60 own a television, 45 own a radio, and 20 own neither. How many households own both a television and a radio?

Since 20 households own neither, those owning at least one = 100 − 20 = 80, so n(T ∪ R) = 80. Using n(T ∪ R) = n(T) + n(R) − n(T ∩ R): 80 = 60 + 45 − n(T ∩ R), giving n(T ∩ R) = 105 − 80 = 25.