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 (W) be divided into full time work W_f and part-time work W_p such that W = W_f \cup W_p.

Also, we classify the students (S) as full time students (S_f ) and part-time students (S_p ) where S = S_f \cup S_p.

We wish to investigate the relation between S and  W.

Accordingly, we interpret Statement 1 as

Statement 2: Full time students can (only) take part-time work (in University) i.e. S_f \to W_p .

By contrapositive,

Statement 3: Non-part-time work (in University) can be carried out by non-full-time students i.e.  \bar{W_p} \to \bar{S_f}.

Since \bar{W_p} = W_f and \bar{S_f} = S_p, we say,

Statement 4: Full-time work can be carried out by part-time students i.e. {W_f} \to {S_p}.

Lastly, since being lecturer is full-time work in university, you can only be part-time student (postgraduate) in University.

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Special thanks to Tan for helping me proof theory … -_- …