Approach to proving questions

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In summary, the conversation discusses a simple graph theory question and the use of propositional logic in proving a statement. The main question is whether to prove "A implies B" or "not B implies not A."
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ych22
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I was attempting a simple graph theory question.

"Let G=(V,E) be a simple graph with n>=3 vertices and 2n-3 edges. Suppose that every subgraph with m(>=2) vertices has <= 2m-3 edges. Let S be the minimum degree for any vertex in V. Prove that S is either 2 or 3."

So I let A be the statement "G=(V,E) is a simple graph with... has <= 2m-3 edges."
Let B be the statement "S is the minimum degree...either 2 or 3".

Is my job to prove that A->B? Can I prove ~B->~A instead? That is, I want to show that if S is 0,1, or >3 then G cannot be a ... with every subgraph with ...

I am self-learning discrete maths and have some uncertainty in propositional logic.
 
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Yes, proving a statement by proving its contrapositive (proving "A implies B" by proving "not B implies not A") is a standard method of proof.
 

1. How do you approach proving questions?

When approaching proving questions, it is important to first read the question carefully and identify what exactly is being asked. Then, analyze the given information and try to understand the underlying concepts and principles. Next, strategize and plan out how you will approach solving the problem, breaking it down into smaller, more manageable steps if necessary. Finally, use logical reasoning and relevant evidence to support your answer.

2. What strategies can be used to prove a question?

Some common strategies for proving questions include using mathematical principles and formulas, providing logical reasoning and evidence, using visual aids or diagrams, and breaking down the problem into smaller parts to make it more manageable. It is also important to check your work and make sure your answer is logically sound and supported.

3. How important is evidence in proving a question?

Evidence is crucial when proving a question because it provides support and validation for your answer. It helps to show your thought process and how you arrived at your solution. Without evidence, your answer may be seen as less reliable and less convincing.

4. What role does critical thinking play in proving questions?

Critical thinking is essential when proving questions as it involves using analytical and logical skills to evaluate information, identify patterns and connections, and make logical conclusions. It is important to critically assess the given information and use it to support your answer in a logical and convincing way.

5. How can I improve my approach to proving questions?

To improve your approach to proving questions, it is helpful to practice regularly and familiarize yourself with different types of problems. Additionally, it can be beneficial to break down the problem into smaller parts and work through them step by step. Seeking help from a teacher or tutor can also provide valuable insights and strategies for approaching proving questions.

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