Final answer:
Analysis is the activity related to scrutinizing or examining a problem to understand its parts and their relationships.
Step-by-step explanation:
The activity that relates to scrutiny or examination of a given problem is b) Analysis. Analysis involves breaking down a complex topic or substance into smaller parts to gain a better understanding of it. When analyzing, you may look at causes, effects, and relationships between parts to understand the whole. It is different from synthesis, which is about combining parts to form a coherent whole, and deduction and evaluation, which involve reasoning and forming judgments based on evidence and criteria, respectively.