Question

In a certain town, if 60 families own TV sets, 85 own scooters, and 70 own refrigerators, what is the minimum number of families that own all three?

a) 15
b) 5
c) 10
d) 25

Answer 1

That easy a) 15
The number of family owing TV set

Answer 2

The minimum number of families that own all three items (TV sets, scooters, and refrigerators) in the town is 10. This is based on the principle that the minimum cannot exceed the smallest individual count, which is 60 for TV sets in this case.

Step-by-step explanation:

The question concerns finding the minimum number of families that own all three items: TV sets, scooters, and refrigerators in a certain town. This is a classic example of an application of the Principle of Inclusion-Exclusion in combinatorial mathematics, which can be used to calculate the overlap between different sets.

However, since the question does not provide information about how many families there are in total or how these items are distributed among the families, we cannot apply the Principle of Inclusion-Exclusion directly. Instead, we can use the property that the minimum number of families owning all three can't be more than the smallest number of families owning just one of the items.

Since the smallest number provided in the question is 60 (families owning TV sets), the minimum number of families that could possibly own all three items is the next number that is common to the sets of families owning each individual item. The only option that is less than or equal to 60 is 'option c) 10'. Therefore, the minimum number of families that own all three is 10 families.