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True But False

A friend (J.G.) sent me this rubric-graded problem, asking how I would answer it.

"Determine if the following statement is true or false: 9878 > 9432 < 9432.78 > 9432 3/4 What would you say?..True or False, no wishy-washy-ness!

The inequality is at best "unstable" and should not be used (as it could lead to future problems).

Technically, it "sounds" correct, given that specific set of numbers, but when you change it, real trouble can arise:

10 > 9 < 11 > 10
Basically, [a < b < c] is the compound statement for [(a < b) and (b < c)], which by transitivity gives you a < c as well. So in your case, you have the general form a < b > c for the compound statement [(a < b) and (b > c)], which precludes inferences on relationship of a and c.

My suggestion was that the statement be broken up for the sake of clarity. But, you may differ...please send me your opinions...

Source: Marzano & Haystead's Making Standards Useful in the Classroom, 2008, p. 31