When the negation sign is outside the parentheses, it affects the entire compound, not just the first component, p. And so on. The truth value of a statement is its truth or falsity. All meaningful statements have truth values, whether they are simple or compound, asserted or negated. A compound statement is truth-functional if its truth value as a whole can be figured out solely on the basis of the truth values of its parts or components.
Negation is a truth-functional operator.
With these four connectives and negation we can express all the truth-functional relations among statements. A truth table is a complete list of the possible truth values of a statement. For example, p is either true or false. But the compound, p q, has 2 components, each of which can be true or false. So there are 4 possible combinations of truth values.