Question

Let W(x,y) mean that student x has visited website y, where the domain for x consists of all students in your school and the domain for y consists of all websites. Express each of these statements by a simple English sentence. ∃x∃y∀z((x ≠ y) ∧ (W(x, z) ↔ W(y, z)))

Answer 1

The statement can be expressed as

There are two different students in your class who have visited the same websites.

Explanation:

Given that

- W(x, y) mean that student x has visited website y.

- The domain of x consists of all students in your school

- The domain of y consists of all website.

It would help to know the meaning of the symbols used, this will help understand the statement better.

- ∧ means conjuction

- ∃ means 'there exists'

- ∀ means 'for all'

- ≠ means 'different from'

- ↔ means 'if and only if'

The statement

∃x∃y∀z((x ≠ y) ∧ (W(x, z) ↔ W(y, z)))

can be expressed as:

There are two different students in your class who have visited the same websites.