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Two Empty Setsby Xidike
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#19
Nov1012, 06:29 AM

P: 345

##\exists x[ (x\in \emptyset\wedge \neg x\in \emptyset')\vee(x\in \emptyset'\wedge \neg x\in \emptyset )]##. 


#20
Nov1012, 06:40 AM

P: 345

If you want a complete formal proof, you must specify which formal system that should be used: which are the axioms and the rules of inference? Is a Hilbert style axiom system (and which variant in this case) or a natural deduction system (and which variant in this case) or some other kind of system? And whatever system is used, complete formal proofs tend to be extremely lengthy. One almost always takes shortcuts. But you have a habit of questioning all possible shortcuts. 


#21
Nov1012, 09:01 AM

P: 35

There is no other way of checking whether your argument is right or wrong. But before anything else let us give the definition of a formal proof. A formal proof is : a finite No of statements ,where each statement is either an axiom or a theorem or a definition or a conclusion by appling a rule of inference on one or more previous statements. 


#22
Nov1012, 10:27 AM

Mentor
P: 18,231

Anyway, the question has been answered. Thread locked. 


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