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 $\displaystyle x \in B$. Remember, that if it is the case that $\displaystyle A \subseteq B$, then for every $\displaystyle x \in A$, we have that $\displaystyle x \in B$. So, pick an $\displaystyle x \in A$ - then, we have that $\displaystyle x = 4c$, but we can rewrite this to $\displaystyle x = 2(2c)$, from which we conclude that $\displaystyle x \in B$, 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 $\displaystyle A\subseteq B$
Where the double arrow means : logically implies