I'm working through the following book: Principles of Mathematics, by Allendoerfer & Oakley. Since I haven't taken a proof-based course yet, and won't be able to until spring 2012 :grumpy:, I want to make sure that I'm not forming habits that will hurt me when I do. There are some answers that aren't provided in the back of the book, so I want to check them with you all. On Page 5, Problem 2: 1. The problem statement, all variables and given/known data Assume that polygon, side of a polygon, angle, length of side, equal, and parallel, have been previously defined. Then define: a) Parallelogram. b) Rhombus. c) Pentagon. d) Regular Pentagon. e) Trapezoid. f) Hexagon. 2. Relevant equations I believe the exercise wants to ensure that I'm using the "if and only if" bi-conditional logical connective correctly. My understanding is that the "if" includes all of the cases that follow the next clause, and "only if" excludes all others. So, I need to make sure that my definitions do not include other polygons. 3. The attempt at a solution Parallelogram: A four-sided polygon is a parallelogram if and only if it has two sets of parallel sides. Rhombus: A four-sided polygon is a rhombus if and only if its sides are equal and has two pairs of congruent angles. Pentagon: A polygon is a pentagon if and only if it has 5 sides. Regular Pentagon: A polygon is a regular pentagon if and only if it has 5 equal sides. Trapezoid: A four-sided polygon is a Trapezoid if and only if it has two parallel sides and two pairs of congruent angles. Hexagon: A polygon is a hexagon if and only if it has 6 sides. Thank you for your help. Edit: I have avoided simply looking up the definitions on the internet so that I'm given the chance to reason my way to an answer, if possible.