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I am really stuck on if there is such an equation. The set given was A={1,2,3,4}. Is it even possible for a relation to be symmetric and antisymmetric, but not reflexive?

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HINT: It doesn’t have to be a total relation. That is, its domain need not be all of $A$.

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Antisymmetric: Assume a relation is antisymmetric unless, aRb and bRa and a≠b.

Symmetric: For all x and y ∈A,if xRy then yRx.

Reflexive: For all x∈A,xRx.

If A={1,2,3,4}, then {(1,1),(2,2)} is antisymmetric, symmetric and irreflexive.

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