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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 (403 points) | 35 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 (4.1k points)
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Answer they gave is A.
S1 is exact representation of it. But S2 seems fine to me.
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how s1 can be correct. It is an OR gate so either one of them can be true.
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