
Re: Inclusive and exclusive definitions... again!
Posted:
Nov 20, 2010 8:54 AM


Just recently experienced another area with an assignment for some teachers where a hierarchical classification of quadrilaterals is also important. For example, asking them which are necessary & sufficient conditions by which to define certain quadrilaterals.
Many got right answers for some questions, but did so by incorrect reasoning and providing incorrect counterexamples! For example, all of them correctly said that 'equal diagonals' is a necessary, but not sufficient condition for a quadrilateral to be rectangle. However, all of them gave as 'counterexample' (to show it is false) a square, but did not realize this was an INVALID counterexample as a square IS a rectangle! They didn't realize they had to produce an example of a quadrilateral that has equal diagonals, but is NOT a rectangle, for example, a general isosceles trapezoid to show that the condition is insufficient.

