I would definitely reason intuitively to solve this question, rather than formally. When I see E(x,y) I paint a picture in my head putting x and y in the same equivalence class:
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| x y |
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When I see !E(y,z) I put a picture in my head where z is outside of the equivalence class of y (and x):
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| x y | | z |
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Hence we can conclude that !E(x,z). So while this is a nice question, I don't think it achieves your goal of testing formal as opposed to intuitive reasoning.
You know about equivalence classes and know to apply them. You can reason about partitions rather than needing to drop down the the level of logical implications (higher level abstractions for the win). If you remove the "think" part and become a little bit more assertive, your intuition becomes a proof.
