This is my first attempt at a proof like this (and even proofs in general) and my textbook gives no direct example for me to compare mine with. Can you examine this and tell me if I have proved what I intended to?
Thank you all.
This is my first attempt at a proof like this (and even proofs in general) and my textbook gives no direct example for me to compare mine with. Can you examine this and tell me if I have proved what I intended to?
Thank you all.
You're more or less right, but there's no need to pick an . Remember, that if it is the case that , then for every , we have that . So, pick an - then, we have that , but we can rewrite this to , from which we conclude that , which satisfies our definition.
I've just put all your ideas into a shorter proof. If this is indeed your first proof, it's an excellent attempt
Remember a proof is a series of logical conclusions, therefor the following proof shows that:
xεA===>( x is an integer divided by 4) ====> (there exists an integer c such that x=4c) ====> (there exists an integer c such that x =2(2c))====> ( there exists an integer d such that x= 2d) =====>(x is an integer divided by 2)====> xεB.
Hence
Where the double arrow means : logically implies