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Topic: Inclusive and exclusive definitions... again!
Replies: 8   Last Post: Apr 1, 2011 3:04 PM

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Michael de Villiers

Posts: 281
Registered: 12/3/04
Re: Inclusive and exclusive definitions... again!
Posted: Nov 20, 2010 8:54 AM
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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 counter-examples! 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 'counter-example' (to show it is false) a square, but did not realize this was an INVALID counter-example 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.

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