DRAFT The Use of Logic in Teaching Proof

Introduction: Even rather simple proofs and disproofs are built atop a normally unexpressed substructure of great logical and linguistic complexity. For example, in [7] I described a number of the many reasoning processes needed to establish the truth or falsity of the following statements: (1) The square of any rational number is rational; (2) For all real numbers a and b, if a> b then a2> b2; and (3) For all real numbers x, if x is irrational then –x is irrational. The articl