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The question reads:

The following describes a world of discourse of flowers:

 Colored flowers are always scented.

 I dislike flowers that are not grown in the open air.

 No flowers grown in the open air, are colorless.

The following fact is provided : This rose is scented.

Use predicate calculus to prove that : I like this rose.

My predicates were:

$\forall$X colored(X) $\implies$ scented(X)

$\forall$X$\lnot$ openAir(X) $\implies$ $\lnot$ i_like(X)

$\forall$X openAir(X) $\implies$ colored(X)

scented(r)

So am I missing something, or is there not enough information to prove the question?

user2942952
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    You cannot prove it. You can verify simply without quantifiers; try with a valuation $v$ such that $(v(\text {i_like}(r))=$ f and check that you can satisfy all the premises. – Mauro ALLEGRANZA Mar 17 '17 at 07:50
  • You're correct. There is no way to prove from the information provided that you like any flower given any other information about it. All of the implications you would need are reversed for some bizarre reason. – Qiaochu Yuan Mar 17 '17 at 07:51

1 Answers1

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There is not enough information to prove you like the rose. From $\forall X\text{ coloured} (X)\Rightarrow \text{scented} (X)$ alone, for instance, it's possible to have $\lnot \text{coloured}(r)\land \text{scented}(r)$.

Shaun
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