The question revolves around the techniques of Scientific Management, particularly in setting a standard task through various studies. To understand which technique involves the study of time, motion, and fatigue, let's explore the given options:
- Method Study: This technique focuses on finding the best method to perform a task by analyzing and designing the most efficient way to do it. However, it does not explicitly involve all three aspects: time, motion, and fatigue.
- Fatigue Study: As the name suggests, this study focuses solely on understanding how workers' efficiency can be improved by reducing fatigue. While it considers worker fatigue, it does not cover the comprehensive analysis of time and motion.
- Work Study: This technique is comprehensive as it combines both Method Study and Work Measurement (including Time Study and Motion Study). It aims to improve the efficiency and productivity of any task by studying the time taken and the motions involved, along with worker fatigue. Therefore, it encompasses all three elements: time study, motion study, and fatigue study.
- Motion Study: This focuses on analyzing the motions necessary to perform a task with the aim of eliminating unnecessary movements. While it is a part of Work Study, it does not address time and fatigue explicitly.
From the above analysis, the correct technique that involves the study of time, motion, and fatigue to set a standard task is \(\text{Work Study}\). Therefore, the correct answer is Option (c) \(\text{Work Study}\).