Venn Diagram for Exercises, Swimming, and Cycling

The question asks to find the Venn diagram that best represents the relationship between the classes: Swimming, Cycling, and Exercises.

Analysis of Relationships:

• Exercises is a broad category that encompasses various physical activities.
• Swimming is a specific type of physical activity and thus a form of exercise. Mathematically, Swimming is a subset of Exercises ($S \subset E$).
• Cycling is also a specific type of physical activity and hence a form of exercise. Mathematically, Cycling is a subset of Exercises ($C \subset E$).
• Swimming and Cycling are distinct activities. While both are exercises, one does not inherently include the other. Therefore, the sets for Swimming and Cycling are disjoint (do not overlap). Mathematically, the intersection is empty ($S \cap C = \emptyset$).

Venn Diagram Representation:

Based on the analysis, the Venn diagram should feature a large circle representing 'Exercises'. Inside this large circle, there should be two smaller circles representing 'Swimming' and 'Cycling'. These two smaller circles should be completely separate from each other, indicating no overlap.

The Venn diagram matching this description is shown in Option 2.

Correct Diagram:

The image associated with Option B correctly depicts this relationship:

This diagram shows 'Exercises' as the encompassing set, with 'Swimming' and 'Cycling' represented as non-overlapping subsets within it.