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Which of the following first order logic statement is equivalent to below statement ? 
If anyone cheats, everyone suffers.  

S1: \forall x (\text{cheat(x)}\rightarrow \forall y \text{ suffer (y)})

S2:  \exists x \text{ cheat(x)}\rightarrow \forall y \text{ suffer (y)}

A. Only S1

B. Only S2

C. Both S1 and S2

D. None 

in Mathematical Logic by (290 points) | 19 views

1 Answer

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S1: For all x ( either x does not cheats OR everyone will suffer) so it is not correct representation since everyone can suffer even if x does not cheats.

S2:If there exist at least one $x$ that cheats then everyone suffers.

so  only S2 is correct.
by (3.7k points)
Answer they gave is A.
S1 is exact representation of it. But S2 seems fine to me.
how s1 can be correct. It is an OR gate so either one of them can be true.
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