LPC1: Decision Procedure I -The Truth-Table Method 1
Consider what you do when you draw up a matrix in order to work out the truth-table for a wff of PC. You set down all possible assignments of truth-values to the simplest propositional elements of the wff – i.e. those propositional elements of which the wff is a truth-function. Let us call these elements the basic formulae of the wff. In PC the basic formulae of a wff are just the propositional variables that occur in it. They are independent of one another in the sense that, in constructing the matrix, no assignment of a particular truth-value to one basic formula commits us to any particular assignment for any of the others. That is, every combination of truth-values represents a logical possibility.