Question

A P implies Q question: If the number b is larger than the number a, then their average (a+b)/2 is larger than a. How would you do this without actually plugging in any numbers?

Answer 1

You could plug some numbers in just to convince yourself that this statement is true.
You should be using inequality symbols when showing that it is true. ie >, <, etc.

Answer 2

Yes but I need to write a proof of how P implies Q. P is the hypothesis that b>a and the conclusion is Q that (a+b)/2 > a.

Answer 3

You need to maybe read a book called "Math Proofs Demystified by Stan Gibilisco".
It will explain the different types of proofs and methods. If you are beginning a study of mathematics on the undergrad level, this will be one of the easiest proofs given to you to write. Proofs get tougher as you go, so practice writing them when you can. I wish I could help you but it has been a long time since I have written any proofs.
You do need let statements.
example: Let b>a. Also you are probably doing basic algebra to create the conclusion of (a+b)/2>a. ie commutative property, distributive property, etc.
You might want to check out the book and prehaps get in an actual study group from students from your class. Good luck, your journey in mathematics has just begun.