  We develop a theory of formal multivariate polynomials over commutative rings
by treating them as ring terms. Our main result is that two ring terms are
s-equivalent (when expanded they yield the same standard polynomial) iff they
are f-equivalent (one can be transformed in the other by a series of elementary
transformations). We consider in a similar way Boolean terms (formulas) and
prove a theorem that two events $a$ and $b$ in a probability space, which are
built by two Boolean terms from respective tuples $A$ and $B$ of elementary
events, are independent if the events in $A$ are independent of the events in
$B$. This theorem rigorizes arguments in the Probabilistic Method in
Combinatorics.
