I have propositional variables $x_1,x_2,x_3,x_4$ and the following Boolean formula:
$$\phi = x_1 \lor x_2 \land (x_3 \land x_4) \land \neg (x_1 \land x_2)$$
Apparently the satisfying assignments are $x_1,x_3,x_4$ and $x_2,x_3,x_4$.
However I am not clear as to why this is not $x_1$ and $x_2,x_3,x_4$.
It seems that there is a convention that we group all expressions with an $\lor$ between them, irrespective of the appearance of parentheses? Because otherwise we could certainly have a lonely $x_1$ ?