For a NOT gate if $x_1$ is input and $x_2$ is the corresponding output, I see the equivalent CNF (conjunctive normal form) is $(x_1 \lor x_2) \land (\overline x_1 \lor \overline x_2)$.
My expectations was that the CNF should not include $x_2$ as it is the output of the gate. I was rather hoping the formula to be of a form $x_2=F(x_1, b_1, b_2, ...)$ where $b_1$, $b_2$, .. are the boolean constants such that when $x_1$ is zero, the $F(.,.,..)$ would yield true just like the NOT gate.
Can anyone help me understand, how come this CNF including $x_2$ is equivalent to a NOT gate. How to draw a truth table for this CNF form as in what value to assign for $x_2$!