Context Free Languages, Pumping Lemma

[dopeyranger]

Hello fellow mathematicians/computer-scientists!

I have a question:

If a subset of a language is not context free, does that mean the language itself is not context-free?

For example, I want to show that the following is not context free, using the pumping lemma:

L = {\omega \in {a,b,c}* | \omega has an equal # of a's, b's, and c's}

And since T ={a^{n}b^{n}c^{n} | n \geq 0} \subset L

If I show that T is not context free, does that show that L is not context free?

 

[Hurkyl]

The language of all strings is context-free (even regular), right? ...