I think this question about predicate calculus logic I got in a test was impossible to solve, please tell me if I'm missing something...

Question

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?

Answer 1

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 $\lnot \text{coloured}(r)\land \text{scented}(r)$.