Just finished untwisting a puzzle into the word induct, which made me think of induce. Are these two words related? (Yes, I could LIU but I need to get off the computer now; will do it myself if I have to.) Also, I am not sure if I used the word cognate correctly.

Yup. And induction, too. They're all from the Latin indūcere.

all from the Latin indūcere.

Meaning, literally 'to lead in'. From in- 'in' + dūcō (dūxi, dūctum) 'to lead'.