Statement 1: A full-time candidate for the degree may be permitted to undertake part-time work in the University subject to such conditions as may be prescribed by the University.
Let Work-at-University () be divided into full time work and part-time work such that .
Also, we classify the students () as full time students () and part-time students () where .
We wish to investigate the relation between and .
Accordingly, we interpret Statement 1 as
Statement 2: Full time students can (only) take part-time work (in University) i.e. .
Statement 3: Non-part-time work (in University) can be carried out by non-full-time students i.e. .
Since and , we say,
Statement 4: Full-time work can be carried out by part-time students i.e. .
Lastly, since being lecturer is full-time work in university, you can only be part-time student (postgraduate) in University.
Special thanks to Tan for helping me proof theory … -_- …