A Generalization of a Theorem of Quine for Simplifying Truth Functions

A method of Quine for identifying the core prime implicants of a given truth function, without obtaining all its prime implicants, is generalized under the so-called ``don´t care´´ conditions. It is shown that our method is equivalent to, and sometimes an improvement of, a result of Roth. When all the prime implicants (under the don´t care conditions) of a truth function are given, our method becomes a generalization of a result of Ghazala and is equivalent to another result of Roth. It is also pointed out that our method may be used, in a way similar to using Roth´s, for simplifying truth functions.