BAD syllogism

All dogs have 4 legs.
My cat has 4 legs.
Therefore my cat is a dog.

this is a "bad" syllogism. All dogs do indeed have four legs, but also do cats for example, as stated in the syllogism, but just becuase all dogs or all of any living thing, have something, it doesn't mean that then everything else that have the same traits are dogs, or that particular living thing. In the above diagram it shows how the logic or fallacy occurs in a syllogism. In conclusion of the diagram we see that SP and SMP are both in the S circle and P Circle, so Sp and SMP are both true in relation to S and P. This is the reasoning behind syllogisms but, for me, its a false form of reasoning becuase two things may have the same trait as i showed above, and not neecesarily be the same thing.

We must do something.
This is something.
Therefore we must do this.

This syllogism is great, its a continous syllogism because once you do something then you keep on doing sosmething, because you always are doing something. So far we've see two syllogism and a diagram showing the logic of the latter.
so we know that a syllogism is a pattern of deductive reasoning involving two premises and a conclusion. A bad syllogism gets the conclusion from the prior premises in a manner which doesn't necessarily follow. Also a syllogism may be correct in the conclusion but not in the prior sentences conjuring to the conclusion. So saying a bad syllogism which may mean a false syllogism is incorrect, the correct way to state if a syllogism is "bad" would be using the word invalid.