Exercise 4

Let $C(x)$ denote the predicate “$x$ is in the correct place”, let $E(x)$ denote “$x$ is in excellent condition”, and let $T(x)$ denote “$x$ is a tool” where the domain of each predicate is the set of objects in a garage. Translate each into plain English:

1. $\exists x \neg C(x)$
2. $\exists x (T(x) \land \neg C(x))$
3. $\forall x (T(x) \to (C(x) \land E(x)))$