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Find a common domain for the variables x, y, and z for which the statement ∀x∀y((x ≠ y) → ∀z((z = x) ∨ (z = y))) is true and another domain for which it is false.

Answer :

The common domain for the variables is; It is true on every set with no more than 22 members and false on other sets.

What is the domain of the variables?

We are given the statement;

∀x∀y((x ≠ y) → ∀z((z = x) ∨ (z = y)))

Since x and y are different objects in the domain, then we can say that anything in the domain is equal to x or to y.

Now, If the domain M has two elements, it means that the given sentence will obviously hold. Also, a one-element domain will work since there wouldn't be a pair x, y such that x ≠ y.

We can conclude that the common domain for the variables is; It is true on every set with no more than 22 members and false on other sets.

An example is that it is true on {a,b} and false on R

Read more about domain of variables at; https://brainly.com/question/11860069

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