I'm having a hard time translating logic statements into english because most of the time I don't know how to translate a pattern I have not seen before:
There are two relations where
- $lecturer(x)$ x is a lecturer
- $human(x)$ x is a human
I find it extremely difficult to work out what a statement is saying if I change a quantifer or remove the brackets, for example is the following correct?
$$\forall x lecturer(x) \to \forall x human(x)$$ If everything is a lecturer then everything is human?
What is the difference between
$$\forall x (lecturer(x) \to human(x))$$
$$\forall x lecturer(x) \to human(x)$$ ?
I don't think the second one is correct in the sense that you cannot write that but how can I tell? Are there any tips for translating statements? I understand the common patterns such as
$$\forall x (A \to B)$$ $$\exists x (A \wedge B)$$
It's just uncommon ones that confuse me or when I start to wonder what will this mean if I remove this bracket? Logic is really my weakpoint.