Given
- $C(x)$ is “$x$ is a cat”
- $S(x)$ is “$x$ is shy”
- $T(x)$ is “$x$ is happy”
translate the following sentence to predicate logic
If any cat is shy, then it is not happy.
This is what I came up with
$$\forall x \left[(C(x) \land S(x)) \to \neg T(x)\right]$$
Seems correct to me but can anyone else offer some insight? Thanks!
To translate this sentence, you can write ∀x ∈ C(x), S(x) → ¬T(x). I believe that what you have written is correct.