I am trying to say: Every a in A is in B

Is the following notation correct?

[(universal quantifier) a (epsilon) A] (epsilon) B

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- Jun 4th 2010, 10:53 AMNoxideNotation
I am trying to say: Every a in A is in B

Is the following notation correct?

[(universal quantifier) a (epsilon) A] (epsilon) B - Jun 4th 2010, 11:05 AMundefined
- Jun 4th 2010, 11:24 AMNoxide
- Jun 4th 2010, 11:36 AMundefined
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.