Set Theory And Types Of Sets

To solve the problem, we need to understand the relationship between the set of continuous functions (A) and differentiable functions (B).

1. Mathematical Insight:
- Every differentiable function is continuous.
- However, not every continuous function is differentiable (e.g., is continuous but not differentiable at ).

This means the set of differentiable functions (B) is a subset of the set of continuous functions (A).

2. Diagram Interpretation:
We are looking for a diagram where the set B (differentiable functions) is completely inside set A (continuous functions).

3. Evaluate the Options:
- Option (A): Set B is inside A — ✔️
- Option (B): Set A is inside B — ❌
- Option (C): A and B overlap partially — ❌
- Option (D): A and B are disjoint — ❌

Final Answer:
The correct option is (A), where the set of differentiable functions is completely contained within the set of continuous functions.