# Is the language in the description context free? [closed]

I am stuck on a question. Lets say there is a string that can be created from three alphabets a,b,c the condition is number of a<= number of b<= number of c. I can solve if there are a and b (two alphabets) but I am not able to solve for 3. Any help will be appreciated. Thanks

• Your language is not context free. Nov 11 '17 at 22:15
• Possible duplicate of How to prove that a language is not context-free? Nov 12 '17 at 0:36
• The title you have chosen is not well suited to representing your question. Please take some time to improve it; we have collected some advice here. Thank you!
– Raphael
Nov 12 '17 at 21:09
• I have a hard time to find even a question here. People have been guessing you're trying to ask for a PDA for the given language. Is that what you want?
– Raphael
Nov 12 '17 at 21:11

The example you give illustrates this. Thus, $\{ w\in\{a,b,c\}^* \mid |w|_a \le |w|_b\}$ is context-free, and similarly, so is $\{ w\in\{a,b,c\}^* \mid |w|_b \le |w|_c\}$. The intersection of these two languages $\{ w\in\{a,b,c\}^* \mid |w|_a \le |w|_b \le |w|_c\}$ is not context-free.