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

Explanation:

Step1: Recall set - operation definitions

The union ($\cup$) of two sets contains all the elements that are in either set. The intersection ($\cap$) of two sets contains all the elements that are in both sets. An empty set has no elements.

Step2: Analyze each option

• For "motor $\cup$ manual": The union of the set of children who used motor - ized scooters and the set of children who used manual scooters will include the elements in the "motor" circle, the "manual" circle, and their intersection. So it is not an empty set.
• For "motor $\cup$ bicycle": The union of the set of children who used motor - ized scooters and the set of children who used bicycles will include the elements in the "motor" circle, the "bicycle" circle, and their intersection. So it is not an empty set.
• For "motor $\cap$ manual": The intersection of the set of children who used motor - ized scooters and the set of children who used manual scooters has 24 elements (the overlapping part of the "motor" and "manual" circles). So it is not an empty set.
• For "motor $\cap$ bicycle": Looking at the Venn - diagram, there is no overlapping region between the "motor" circle and the "bicycle" circle, which means there are no children who used both motor - ized scooters and bicycles. So this intersection represents the empty set.

Answer:

motor $\cap$ bicycle