Fizz Buzz For Mathematicians

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To this end an initial "bozo-filter" is sometimes applied, wherein a candidate is asked to write some utterly trivial code to demonstrate that they have at least a basic grasp of how to write programs. A common test is the "FizzBuzz" test - go look it up.

So I was idly speculating - what would be a similar initial filter for "Mathematician"? This is clearly an impossible question, because we don't actually know what a mathematician is, nor do we really know what a mathematician does. However, we don't actually know what programmers do either, so maybe that's OK.

One possibility that came to mind is this question:

• An "equivalence relation" on a set X is a function
  
  $E:X{\times}X\rightarrow\{T,F}$
  that satisfies these three conditions:
• For all x in X, E(x,x)=T,
• For all x and y in X, E(x,y)=E(y,x),
• If E(x,y)=T and E(y,z)=T, then E(x,z)=T.

• Suppose E(x,y)=F and E(y,z)=T. What can you say about E(x,z) ?
• Prove it.

Can you?

• [0] http://www.codinghorror.com/blog/2007/02/why-cant-programmers-program.html
• [1] http://www.globalnerdy.com/2012/11/15/fizzbuzz-still-works/