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MathNet 2013 Question 94

Math Olympiad Vault · MathNet 2013

Question 94

On planet Automoria there live a (possible infinite) number Automorians. Any Automorian have feelings like love and respect. It is known that
1) each Automorian loves exactly one Automorian and respects exactly one Automorian;
2) if $A$ loves $B$, then every Automorian respecting $A$ also loves $B$;
3) if $A$ respects $B$, then every Automorian loving $A$ also respects $B$;
4) for every Automorian there is somebody loving him.
Is it true that every Automorian respects the Automorian he loves?