Here is one way to show this using natural deduction. Of the rules, I used contradiction introduction (⊥I) which I did not see on your list, but I suspect is permitted because reduction ad absurdum is permitted.
On line 1 is the assumption. I attempted an indirect proof (IP) or reductio ad absurdum beginning on the second line. This completed on line 10 which also completed the proof.
In between I assumed "P" in a subproof and then immediately assumed "¬Q" in another subproof. In line 5 I combined these two assumptions to get "P ∧ ¬Q" on line 5. That contradicted the assumption on line 2 and I completed an indirect proof on line 7 discharging the "¬Q" assumption on line 4. The set of lines from 3 to 7 represented a conditional introduction (→I) or conditional proof on line 8 which allowed me to discharge the "P" assumption in line 3. That contradicted line 1 and so I introduced a contradiction in line 9.
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/