The Tautologies over a Finite Set are Context-Free

In this note we show, that the set of valid boolean formulae over a nite set of variables is a natural example for a context-free language. Context-free languages are very important in computer science. Thus it would be nice to enlarge the collection of natural and attractive examples. One interesting example is obtained by the question whether the set of tautologies over a xed nite set of variables is context-free 1. We show that the answer of this question is positive. The proof of this fact is very simple. However, up to our knowledge, this fact is not available in the (standard) literature. Therefore this note might be of interest.