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> Why is $\forall xO(x,c), \forall xO(c,x) \therefore \forall xO(x,x)$ an invalid reasoning?
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This exercise appears in P.D. Magnus. *"forallX: an Introduction to Formal Logic"* (p. 268, exercise D. 7).

I think to satisfy both universal quantifiers, predicate $O$ must be symmetric, so I cannot find an interpretation that makes $\forall xO(x,x)$ false. On the surface, it seems a valid reasoning (considering a non-empty universe). 

What's happening here?