3. This problem is about the logic S. The sentences in this logic are All x are y and Some x are y. We used a certain canonical model M2. Starting with a set I of sentences in the logic, we took M, to be the set of all Some-sentences in I. For a noun u, we said: [u] = { M2 : one or both of the nouns in p is ss u} = {"Some x are y" in I: either I + All x are u or I + All y are u} Suppose we change the model. Let M2.5 have the same universe M2. But for the nouns, let's say {q M2 : both of the two nouns in q are ss u} {"Some x are y" in 1:1 + All x are u and also I + All y are u} (a) Prove that M2.5 satisfies the All-sentences in T. (b) Find a set I where M25 does not satisfy the Some-sentences in T. [Hint: I has to have a Some-sentence. But if you take a "random set I with two or three Some-sentences and one All-sentence, I bet that your M2.5 XI some.] 3. This problem is about the logic S. The sentences in this logic are All x are y and Some x are y. We used a certain canonical model M2. Starting with a set I of sentences in the logic, we took M, to be the set of all Some-sentences in I. For a noun u, we said: [u] = { M2 : one or both of the nouns in p is ss u} = {"Some x are y" in I: either I + All x are u or I + All y are u} Suppose we change the model. Let M2.5 have the same universe M2. But for the nouns, let's say {q M2 : both of the two nouns in q are ss u} {"Some x are y" in 1:1 + All x are u and also I + All y are u} (a) Prove that M2.5 satisfies the All-sentences in T. (b) Find a set I where M25 does not satisfy the Some-sentences in T. [Hint: I has to have a Some-sentence. But if you take a "random set I with two or three Some-sentences and one All-sentence, I bet that your M2.5 XI some.]