47. find the error in the "proof" of the following "theorem." "theorem": let r be a relation on a set a that is symmet- ric and transitive. then r is reflexive. "proof": let a e a. take an element be a such that (a, b) e r. because r is symmetric, we also have (b, a) e r. now using the transitive property, we can conclude that (a, a) e r because (a, b) e r and (b, a) e r.