Answer
a) $\exists x \neg P(x)$
b) $\forall x (P(x) \land R(x))$
c) $\forall x (P(x) \land R(x))$
d) $\neg \forall x (P(x) \land R(x))$
e) $\forall x (\neg P(x) \land R(x))$
Work Step by Step
a) Let. P(x) mean " x is in the correct place" .
$\exists x \neg P(x)$
b)Let P{x) mean "x is in the correct place“. Let R(x) mean "x is in excellent condition".
The domain of x are tools.
$\forall x (P(x) \land R(x))$
c) Let P{x) mean "x is in the correct place“. Let R(x) mean "x is in excellent condition".
$\forall x (P(x) \land R(x))$
d) Let P{x) mean "x is in the correct place“. Let R(x) mean "x is in excellent condition".
The domain of x are tools.
$\neg \forall x (P(x) \land R(x))$
Nothing means that there does not exists.
e) Let P{x) mean "x is in the correct place“. Let R(x) mean "x is in excellent condition".
But can be taken as "and".
$\forall x (\neg P(x) \land R(x))$
