Notice that it is not possible (assuming all of the trivial qualifying criteria are supplied) to be in Arches and not be in Utah. However, one can be in Utah while not in Arches National Park. The implication only works in one direction. Statements (1) and (2) taken together imply statement (3). Statement (3) does not imply anything about statements (1) or (2). Notice that we have not proven statement (3), but we have shown that statements (1) and (2) together imply statement (3). In mathematics, what is proven is not the truth of a particular theorem, but that the axioms of the system imply the theorem. In other words, it is impossible for the axioms to be true and the theorem to be false. The strength of deductive systems is that they are sure of their results. The weakness is that they are abstract constructs which are, unfortunately, one step removed from the physical world. They are very useful, however, as mathematics has provided great insights into natural science by providing useful models of natural phenomena. One result is the development of products and processes that benefit mankind.