Citation: James H. Hughes (2022) Logical Equivalence Failure, International Journal of Mathematics and Statistics Studies, Vol.10, No.2, pp.1-25
Abstract: As a point of mathematical logic, this paper proves that the contrapositive is not logically equivalent to the conditional, which disproves the “proof by contradiction” that has been used in mathematics for over a hundred years. The paper then provides suggestions for why the “proof by contradiction” may have been derived in error.
Keywords: Conditional, Logic, Mathematics, Venn diagram., contrapositive, proof by contradiction
