How to connect statements in predicate logic? I have the following logical riddle:

"All cats are animals. Everything small is colorful." 
Which of the following assertions can be derived from this? Please justify the steps.  a) All colorful cats are small animals.  b) Some small cats are not colorful animals.  c) All small cats are colorful animals.  d) All non-colorful cats are animals that are not small.


I am confused because it seems to me that the statements do not match. I understand that I can use the objects in the statements like: A: Cat;
B: Animals;
C: Small;
D: Colorful.
and write:
A->B
C->D
I also understand how to translate the statements a-d into logical statements. e.g.
a) (A&D)->(B&C)
etc. What I do not understand is how to reason / decide if this is possible with the above statements or not since I don't see a connection between A and D for instance. So I have two questions: 1. Is my approach correct or am I making a basic mistake? and 2. How can I argue to get the solution?
Thanks for any help in advance!
A: The Venn diagram

with legend

*

*A: animals

*T: cats

*F: colorful

*S: small

represents the premises “All cats are animals. Everything small is colorful.”
From the diagram, it is evident that the given premises entail conclusions (c) & (d), but not conclusions (a) & (b).

Addendum in response to the first comment below:

Deriving conclusion (d) (Line $8$) for example, from the two premises (Lines $1$ & $2$) using a Fitch-style proof (note that here, Tx, Mx, Sx, and Fx mean “x is a cat”, “x is an animal”, “x is small” and “x is colorful”, respectively) can involve a truth table to verify that Line $6$ is a tautological consequence of Lines $3-5.$
But your intuition is correct: truth tables alone are inadequate to assess the validity of categorical arguments. For example, the categorical sentence “all cats are animals” is suitably formulated as the quantified sentence $\forall x [T(x)\rightarrow M(x)],$ but a truth table only admits its truth-functional form (the non-quantified sentence) $P,$ which clearly captures insufficient nuance. Although truth tables reveal whether a sentence is tautological, they don't generally reveal the validity of a sentence. (Assessing the validity of an argument means assessing the validity of its corresponding conditional sentence <premise>$\rightarrow$<conclusion>.)
