Question

1. Here is a model:

Domain: {Wikipedia, 2, Isaac Newton}

Referents: ​n​: Isaac Newton

Extensions: P: Ø Q: {2} R: {Wikipedia, Isaac Newton}

Is the following proposition true or false on this model? Explain your answer.

∀​x​(​Qx ​∨​Rx​) → ​Pn

2. Is the following argument valid or invalid? If it is valid, explain why there cannot be a countermodel. If it is invalid, provide a countermodel.

ᄀ∀​xHx

∃​xMx

∴ᄀ​∃​x​(​Mx ​∧​Hx​)

Answer 1

Solution:-

Given that

1. Is the following proposition true or false on this model? Explain your answer.

The proposition is false

This proposition is an implication and an implication

is false if and only if A is true and B is false.

In this case, since = {Wikipedia, 2, Isaac Newton} = Domain

then is true

and since the extension of P is empty then Pn is false.

Therefore is false.

2. Is the following argument valid or invalid? If it is valid, explain why there cannot be a countermodel. If it is invalid, provide a countermodel.

The argument is invalid

Countermodel:

Domain = {1, 2, 3}

Extensions: M: {1, 2} H: {2, 3}

With this model, both premises are true but the conclusion is false

¬ is true because the extension of H is not equal to the domain

is true because the extension of M is not empty

¬ is false because 2 is in both the extension of M and the extension of H

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