Fizz Buzz For Mathematicians 

It's wellknown (for some definition of "wellknown") and
deeply controversial that 80% (some say 90%) of applicants
for programmer jobs can't actually program[0][1]. Recruiting
good programmers (for some definition of "good") is a known
"Hard Problem(tm)"
To this end an initial "bozofilter" 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.
Problem is, I wonder if too many nonmathematicians can pass
this test to make it of any value.
Can you?
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