I am having trouble with this problem:
Let N3SAT denote the non-satisfiability problem for 3CNF’s. Show that $N3SAT\leq_p UNQ$ where in UNQ, given a CNF φ we want to know whether there is a unique satisfying assignment for φ.
I am given a hint that for every 3CNF ψ, I should construct a CNF φ (in polytime) such that ψ is a NO input for 3SAT if and only if φ is a YES input for UNQ.
What I'm having problem with is constructing the CNF from a 3CNF. Isn't a 3CNF just a case of a CNF.
So, from what I understand, once I get a CNF φ that gives a yes for UNQ, then that corresponding 3CNF will give a NO for 3SAT. So somehow the truth assignments will work out in a way that both conditions are solved.
Can someone help me out?