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Puzzling

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    $\begingroup$ @Pranay you do need to prove that that solution is always possible though. It could be the case that there are no menu combos with one dish. $\endgroup$ Commented yesterday
  • $\begingroup$ @Goblin. Ah I see. I see that we are only told what the combos satisfy, but we aren’t told what the combos themselves are. Nice! $\endgroup$ Commented yesterday
  • 1
    $\begingroup$ @florianF no other. $\endgroup$ Commented yesterday
  • 1
    $\begingroup$ Why do we need property 1? Properties 1 and 3 imply the empty set, which we might as well choose to be Combo of the Year every year. It seems we can just do away with this by taking property 1 to be assuredly false. $\endgroup$ Commented yesterday
  • 1
    $\begingroup$ Since $M\cup M'=\mathcal U$, properties 2 and 3 imply property 1, and so also the empty set as this is $(M\cup M')'$. $\endgroup$ Commented 20 hours ago