Gatebook: Logic

Question 1

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

Question 2

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.

Question 3

Answer they gave is A.
S1 is exact representation of it. But S2 seems fine to me.

Question 4

how s1 can be correct. It is an OR gate so either one of them can be true.

Satbir · Answer 1 · 2019-09-28T15:45:56+0000

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.

Answer they gave is A.
S1 is exact representation of it. But S2 seems fine to me. — Sambhrant Maurya, Sep 28
how s1 can be correct. It is an OR gate so either one of them can be true. — Satbir, Sep 28

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Gatebook: Logic

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