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Oct 28, 2019 at 20:27 comment added rici All of your solutions produce the sentences $a^i$ and $b^i$ for $i\ge 1$, although the OP requests $a^ib^j, i,j\ge 1, i\ne j$. Of course, the fixes are minor. For the first one, you can change $T\to aTb\mid\epsilon$ to $T\to aTb\mid ab$.
Oct 28, 2019 at 19:49 vote accept Florian Ludewig
Oct 28, 2019 at 8:05 history answered Yuval Filmus CC BY-SA 4.0