# Context Free Languages, Pumping Lemma

1. Mar 9, 2012

### 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?

2. Mar 9, 2012

### Hurkyl

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