Question

Let K(x, y) denote the statement x knows y and D denote the domain of all people. Express the following English sentences as a quantified proposition using the definitions above

There is somebody that no one knows.

Answer 1

The English sentence 'There is somebody that no one knows' can be translated into a quantified proposition as ∃x ∈ D (∀y ∈ D (¬K(y, x))), which indicates there exists an individual who is not known by anyone else.

Step-by-step explanation:

The statement 'There is somebody that no one knows' in terms of quantified propositions using the provided definition for D as the domain of all people and K(x, y) as the statement 'x knows y', can be expressed in symbolic logic as:

∃x ∈ D (∀y ∈ D (¬K(y, x)))

This reads as 'There exists an x in the domain of people such that for all y in the domain of people, it is not the case that y knows x.' It reflects the concept that in set of all people, at least one person exists who is not known by any other person