Question 161692: Can you tell me how to work a proof? I don't understand them at all. Mostly I don't understand how you know what the next step is going to be. So, I need help with these very much. Can you show me an example and explain it as you go along? I would really appreciate this.
Thank you.
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! Proofs are actually really really tricky, especially when you are just getting introduced to them, and especially because in high school a lot of the proofs you are doing seem so silly (like proving things that are obvious from a diagram). You need to use theorems and definitions that you know are true in order to prove to the world that some other statement is definitely true. Usually, you are given one or more random statements. Those are the statements you usually start with, and can assume are true. You are also given some other statement to prove. For instance, the problem might say "Given: Bob lives in Boston." and "Prove: Bob lives in America." You also know these statements are true (theorems, postulates, definitions, anything like that): "Boston is the capital of the state of Massachusetts," "A state's capital is in that state," and "Massachusetts is in America." So the 2-column proof would look like this:
Statements__________________________Reasons
1. Bob lives in Boston._____________1. Given
2. Bob lives in the capital of MA.__2. Boston is the capital of MA.
3. Bob lives in MA._________________3. A state's capital is in that state.
4. Bob lives in America.____________4. Massachusetts is in America.
So you usually start with the Given. Then take any true thing you know about that given thing. So here I knew Boston was the capital of MA, but nothing else about Boston. So I couldn't jump right to number 4 from number 1 because I had no reason to back that up. When you read your statements, you should be able to kind of tell a story. So my story would be: "Bob lives in Boston. So Bob lives in the capital of MA. So Bob lives in MA. So Bob lives in America."
Then at any point, if someone asks "How do you know?", you give them the reason. I hope that makes some sense. Remember, there are often many different ways to prove the same thing, especially once you know a lot of different theorems and definitions. Good luck!!!
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