Yes, you can definitely use legal reasoning and logical arguments in your answers for the UPSC Law Optional Subject Exam. In fact, it is highly recommended to utilize these skills as they are crucial for demonstrating your understanding of the subject matter and your ability to critically analyze legal issues.

Using Legal Reasoning:
Legal reasoning involves applying legal principles to a set of facts in order to arrive at a logical conclusion. It requires you to analyze the given legal provisions, case laws, and precedents to form a well-reasoned argument. Here's how you can incorporate legal reasoning in your answers:

1. Identify the legal issues: Begin by identifying the key legal issues raised by the question. This will help you focus your analysis and provide a structured response.

2. Apply legal principles: Use your knowledge of legal principles to analyze the given problem. Explain how the relevant laws, statutes, and constitutional provisions are applicable to the given facts.

3. Argue both sides: Present a balanced approach by considering arguments from both perspectives. This showcases your ability to critically evaluate different viewpoints and make a well-rounded argument.

Using Logical Arguments:
Logical arguments play a vital role in presenting a coherent and persuasive answer. By employing logical reasoning, you can strengthen your arguments and make them more convincing. Here's how you can use logical arguments effectively:

1. Identify relevant facts: Carefully analyze the given facts and determine which ones are crucial to your argument. Highlight these facts to support your reasoning.

2. Establish cause and effect: Clearly establish the cause and effect relationship between the facts and the legal principles. This will help you build a logical chain of reasoning.

3. Organize your arguments: Structure your answer in a logical manner by presenting your arguments in a clear and sequential order. Use headings and subheadings to make your response visually appealing and easy to follow.

4. Support with evidence: Back up your arguments with relevant case laws, statutes, or scholarly articles. This demonstrates your research skills and strengthens the validity of your arguments.

By incorporating legal reasoning and logical arguments in your answers, you showcase your ability to think critically, analyze legal problems, and present a well-reasoned opinion. These skills are highly valued in the field of law and will greatly enhance your performance in the UPSC Law Optional Subject Exam.