Sets Practice Test 1

Concept:Use the inclusion-exclusion principle for two sets to find the intersection when the union, and individual set sizes are known.Explanation:Let $C$ be the set of families having a car.Let $S$ be the set of families having a scooter.Total families $= 2000$.Families with neither $= 73$.So, families with at least one vehicle, $n(C \cup S) = 2000 - 73 = 1927$.Given $n(C) = 849$ and $n(S) = 287$.By inclusion-exclusion, $n(C \cup S) = n(C) + n(S) - n(C \cap S)$.Substitute values: $1927 = 849 + 287 - n(C \cap S)$.So, $1927 = 1136 - n(C \cap S)$.Thus, $n(C \cap S) = 1136 - 1927 = -791$.A negative number of families is impossible.Therefore, the given data is inconsistent, and no valid number of families can have both a car and a scooter.Answer:None of these.