The following "laws" of the propositional calculus are used to "reduce" complex formulas. The "laws" can be verified easily with truth tables. For each law, the principal (outermost) connective is associated with logical equivalence ≡ or identity =. A complete analysis of all 2n combinations of truth-values for its "n" distinct variables will result in a column of 1's (T's) underneath this connective. This finding makes each law, by definition, a tautology. And, for a given law, because its formula on the left and right are equivalent (or identical) they can be substituted for one another.