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How to express these in terms of predicates & quantifiers :

  • Some properties are tautologies
  • The negation of a contradiction is a tautology
  • The dis junction of two contingencies can be a tautology.
  • The conjunction of two tautologies is a tautology.

I could find the answer from the answer key in this sequence as:

  • $\exists xT(x)$
  • $\forall x(C(x)\rightarrow T(\neg x)) $
  • $\exists x\exists y(\neg T(x)\wedge \neg C(x) \wedge \neg T(y) \wedge \neg C(y) \wedge T(x\vee y)) $
  • $\forall x\forall y((T(x) \wedge T(y)) \rightarrow T(x\wedge y))$

From Rosen 5th edition

And not at all able to know how did he arrive at this answer

Can anyone help ? !!

Thanks in advance

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    The logic sentences are fairly straightforward translations of the English statements, can you elaborate what you're stuck with? Are you unfamiliar with the notation, or perhaps how to translate them back to English? Or are you fine with this and there's something deeper that you're stuck on?2012-10-23
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    Yeah @LukeMathieson but as we can see the Second statement it says " The negation of a contradiction is a tautology " i.e it should be "$\forall x(C(\neg x)\rightarrow T(x)) $" next the Statement but i din't get the logic behind Rosen's answer ...2012-10-23

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