2. Non-actor and writer

3. A painter is not a master.

4. Mathematicians are not painters

5.b is not a writer

6. Neither B nor C is a painter.

I know from 6 that Jia is a painter, and from 234 that Jia is not a performer, writer, athlete or mathematician, but a painter and singer.

We know from 5 that B is not a writer, C is a writer, from 2 that B is a performer, and from 1 that C is a mathematician, so C is a mathematician and a writer, and B is an athlete and a performer.

If we bring A, B and C into every family again, if there is no conflict, the reasoning is correct. I didn't test it. See for yourself.