Lucky Deduction?

One rule can be represented: N-->L Another can be represented: Q-->K Both have a common variable with the "either, but not both" rules above. I combined them to read: N--> not P--> L Q--> not J--> K I got the right answer because I figured it had something to do with this deduction, but I don't know why. I could have ran through several scenarios and did it the long way but I took a chance with this deduction. Did I get lucky or can the answer be derived from this chain alone? If it can, how is that so? I figure if I understood the logic behind this I can use it more often.