We consider an infinite particle system, the simple exclusion process, which was introduced in the 1970 paper "Interaction of Markov Processes," by Spitzer. In this system, particles attempt to move independently according to a Markov kernel on a countable set of sites, but any jump which would take a particle to an already occupied site is suppressed. In the case that the Markov kernel is symmetric, an inequality by Liggett gives a comparison, for expectations of positive definite functions, between the exclusion process and a system of independent particles. We apply a special case of this inequality to an auxiliary process, to prove another comparison inequality, and to derive a large deviation result for the symmetric exclusion system. In the special case of simple random walks on $Z$, this result can be transformed into a large deviation result for an infinite network of queues.