Question

Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives

Answer 1

Answer:

A) ∃y(¬P(y))

B) ∀y(P(y) ^ Q(y))

C) ∀y(P(y) ^ Q(y))

D) ¬∃y(P(y) ^ Q(y))

E) ∃y(¬P(y) ^ Q(y))

Step-by-step explanation:

We will use the following symbols to answer the question;

∀ means for all

∃ means there exists

¬ means "not"

^ means "and"

A) Something(y) is not in the correct place is represented by;

∃y(¬P(y))

B) For All tools are in the correct place and are in excellent condition, let all tools in the correct place be P(y) and let all tools in excellent condition be Q(y).

Thus, we have;

∀y(P(y) ^ Q(y))

C) Similar to B above;

∀y(P(y) ^ Q(y))

D) For Nothing is in the correct place and is in excellent condition:

It can be expressed as;

¬∃y(P(y) ^ Q(y))

E) For One of your tools is not in the correct place, but it is in excellent condition:

It can be expressed as;

∃y(¬P(y) ^ Q(y))