Answer:
Let P(x) = x is in the correct place
Let Q(x) = x is in the excellent place
R(x) denotes the tool
Explanation:
a) Something is not in the correct place.
P(x) is that x is in the correct place so negation of ¬P(x) will represent x is not in the correct place. ∃x is an existential quantifier used to represent "for some" and depicts something in the given statement. This statement can be translated into logical expression as follows:
∃x¬P(x)
b) All tools are in the correct place and are in excellent condition.
R(x) represents the tool, P(x) represents x is in correct place and Q(x) shows x is in excellent place. ∀ is used to show that "all" tools and ∧ is used here because tools are in correct place AND are in excellent condition so it depicts both P(x) and Q(x). This statement can be translated into logical expression as follows:
∀ x ( R(x) → (P(x) ∧ Q(x))
c) Everything is in the correct place and in excellent condition.
Here P(x) represents correct place and Q(x) represents excellent condition ∀ represent all and here everything. ∧ means that both the P(x) and Q(x) exist. This statement can be translated into logical expression as follows:
∀ x (P(x) ∧ Q(x)
