# How to construct CFG for language

We have alphabet $\Sigma = \{ { a, b} \}$.

How to construct CFG for language $\Sigma^{\ast} - \{a^{n}b^{n} | n \ge 0 \}$.

I suggest that is very easy, but I can't invent. I know PDA for this language if it can help.

Split into parts that you can handle. All strings not of the form $a^*b^*$. All strings of the form $a^ib^j$ with $i< j$. Then all strings ....