The diagram shows the number of children who have ever used motorized scooters, manual scooters, and/or bicycles.

Question

Circles labeled Motor and Manual overlap. A circle labeled bicycle is to the side of the other 2 circles. Circle Motor contains 8 and circle Manual contains 32. The overlap of the circles contains 24. Circle Bicycle contains 44. Number 3 is on the outside of the circles.

Which combination represents the empty set?

motor ⋃ manual
motor ⋃ bicycle
motor ∩ manual
motor ∩ bicycle

Answer 1

To find which combination represents the empty set, we need to evaluate each option based on the information from the diagram.

1. motor ∪ manual: This represents all children who have used either a motorized scooter or a manual scooter. Since the overlap (those who have used both) is 24, and there are additional users of each (8 in motor and 32 in manual), the total is not empty.

2. motor ∪ bicycle: This represents all children who have used either motorized scooters or bicycles. With motor having users (8 + 24 = 32) and bicycles having 44 users, this set is not empty.

3. motor ∩ manual: This represents children who have used both motorized scooters and manual scooters. Since the overlap is 24, this set certainly is not empty.

4. motor ∩ bicycle: This represents children who have used both motorized scooters and bicycles. Since there is no indication of children using both (the circles for motor and bicycle are separate), the intersection is empty.

Therefore, the combination that represents the empty set is:

motor ∩ bicycle.