To deduce that Roberta is not tall How do I deduce? 
Suppose we know that:


*

*if Paolo is thin, then Carlo is not blonde or Roberta is not tall

*if Roberta is tall then Sandra is lovely

*if Sandra is lovely and Carlo is blonde then Paolo is thin

*Carlo is blonde


Can we deduce that Roberta is not tall?
 A: Yes we can. We would do it by contradiction.
Suppose that Roberta were tall. Then, by the second statement, Sandra is lovely. By the third statement, Paolo is thin. 
By the first statement, either "Carlo is not blonde" or "Roberta is not tall" must be true. But neither of these are.
Hence, we can conclude that Roberta is not tall, which is consistent with the hypotheses. In that case, nothing can be said about either Sandra or Paolo (which is a pity, I'd have loved to know Sandra).
A: Hint: 
You have two options. Roberta is not tall is true or false. If it is false (it means that Roberta is tall) we can deduce from first statement that Paolo is thin is false (how?). This means that Sandra is lovely and Carlo is blonde must be false (from third statement). Since Carlo is blonde is true, Sandra is lovely must be false. Then, from second statement we get that Roberta is tall is false. 
So, if we start with Roberta is tall we obtain Roberta is not tall! Not possible.
Now, you only have to show that Roberta is not tall is possible. 
A: Writing the statements symbolically, using $P$ for "Paolo is thin", $C$ for "Carlo is blonde", $S$ for "Sandra is lovely" and $R$ for "Roberta is tall":
$$P\to(\neg C\lor\neg R)\\
R\to S\\
(S\land C)\to P\\
C$$
Substituting the value of C into the first and third sentences and then simplifying we get
$$P\to\neg R\\
R\to S\\
S\to P$$
These can be chained to get the single proposition
$$R\to\neg R$$
from which follows $\neg R$, i.e. Roberta can be deduced as not tall from the given statements.
A: We know that:


*

*$\text{Thin}(P)\implies\neg\text{Blonde}(C)\vee\neg\text{Tall}(R)$

*$\text{Tall}(R)\implies\text{Lovely}(S)$

*$\text{Lovely}(S)\wedge\text{Blonde}(C)\implies\text{Thin}(P)$

*$\text{Blonde}(C)$ is true



Assume by contradiction that Roberta is tall.
Therefore $\text{Tall}(R)$ is true.
Therefore $\text{Lovely}(S)$ is true.
Therefore, since $\text{Blonde}(C)$ is true, $\text{Thin}(P)$ is true.
Therefore, since $\neg\text{Blonde}(C)$ is false, $\neg\text{Tall}(R)$ is true.
Which contradicts the assumption, hence Roberta is not tall.
