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1)[itex]\forall x\forall y\forall z G(F(F(x,y),z),F(x,F(y,z)))[/itex]

2)[itex]\forall xG(F(x,c),x)[/itex]

3)[itex]\forall x\exists yG(F(x,y),c)[/itex]

4)[itex]\forall x\forall yG(F(x,y),F(y,x))[/itex].

5) [itex]\forall x\forall y\forall z ( G(x,y)\wedge G(x,z)\Longrightarrow G(y,z))[/itex]

Where G is a two place predicate symbol. F ,is a two place term symbol and c is a constant.

Prove :[itex]\exists! y\forall xG(F(x,y),x)[/itex]

[itex]\exists ! y[/itex] means : there exists a unique y

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# Predicate calculus

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