Here are the signals that point to each technique:
"Can reach AND return" → Strongly Connected Components
"Either A or B must be true" → -SAT
"Removing this edge disconnects" → Bridges
"Connect all nodes, minimum cost" → Minimum Spanning Tree
"Dynamic connectivity queries" → Disjoint Set Union
If you see multiple signals, you might need to combine techniques. Read the problem statement twice and check which signal is strongest.