I am trying to say: Every a in A is in B
Is the following notation correct?
[(universal quantifier) a (epsilon) A] (epsilon) B
You could read ":" aloud by simply pausing: "For all a in A, a in B." Or you could read it as "it is true that."
Here's another way.
$\displaystyle A \subseteq B$ if and only if $\displaystyle \forall x(x\in A \Rightarrow x\in B)$
Edit: upon reflection, what I wrote above:
isn't precise enough, because $\displaystyle a$ is unspecified, thus the expression is not a sentence/proposition in the language (it cannot be assigned a truth value); we would still need the $\displaystyle \forall$ symbol, like I did in this post.