Note that in the complex expression involving more than one connective we used parentheses to punctuate the expression so as to make it unambiguous. The arrangement of the parentheses make clear that the statement as a whole is a conjunction, each conditional being limited to the elements in its set of parentheses and so not ranging over the whole proposition. Except for negation, each connective should apply to two propositions, where one or both of these component propositions may itself be a compound proposition marked off by parentheses. Parentheses are used to make clear to which two propositions any such connective applies. The main connective of the proposition as a whole will stand outside all parentheses.
Negation differs only in that it applies to one proposition.
The calculations are based on the definitional tables for each basic connective given above. Truth Tables and Validity Truth tables provide a useful method of testing the validity of any argument. There must be a line for each possible combination of truth values for these components. Each additional component will double the number of lines needed. A single component will need two lines.