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Proof WritingSuperchallengeExistence, Uniqueness and Counterexamples

Existence, Uniqueness and Counterexamples · Superchallenge problem

For how many relations RR on {1,2,3}\{1, 2, 3\} are BOTH "∀x ∃y:(x,y)∈R\forall x\ \exists y: (x, y) \in R" and "∀y ∃x:(x,y)∈R\forall y\ \exists x: (x, y) \in R" true?