Disjoint sets are collections of non-overlapping sets, useful for cycle detection in graphs. Key operations are `find` (determining set membership) and `union` (merging sets). A cycle exists if a graph edge connects nodes within the same set. Efficient implementations use weighted union and path compression (collapsing find) for optimized performance. This segment sets the stage for a practical example of cycle detection. It introduces a sample graph and explains the step-by-step approach to be used for cycle detection using disjoint sets. This segment clearly defines disjoint sets using a non-connected, non-directed graph example. It visually demonstrates how different components of a graph represent disjoint sets, emphasizing that their intersection is an empty set. This segment introduces the 'find' operation in disjoint sets, explaining how to determine which set an element belongs to. The explanation is clear and concise, using the graph example to illustrate the process.This segment focuses on the 'union' operation, showing how connecting components in a graph corresponds to performing a union on the respective sets. It highlights the purpose of the union operation in the context of detecting cycles. This segment concisely explains the crucial components of a node within a disjoint set data structure, including the necessary attributes like index, parent pointer, and next node pointer, providing a clear understanding of its internal organization and how these elements work together. This segment provides a visual representation of disjoint sets using a tree-like structure. It demonstrates how to graphically represent sets and use this representation to efficiently detect cycles within the graph. This segment demonstrates the initial steps of cycle detection in the example graph. It shows how to create sets from edges and perform union operations, building the foundation for the cycle detection process.