ANSWERS: 1

I had ago not sure if this is correct. 5 maximal subsets that do not entail p 1. ¬r ∧ q > p 2. S2 3. ¬r ∧ S 4. q 5. S1 Subsets 1 > 4 do not entail p as their members are not mutually exclusive in a way that would lead to the entailing of p. The 5th maximal subset includes q and claims that p is false. All the sets exclude r and s which means that they don't entail either ¬r or s. Taking a set, S, of sentences and X ⊆ S, X = U X which doesn't entail p. S1 = {¬r,s, ((¬r V q) > p), q} If S1 satisfies 2 conditions, then X ⊆ S1, X ∧ = A and if Y ∩ X Then Y, x can't be false. Therefore if a sentence doesn't entail A then ¬A ⊆ Y Hope this helps 😊
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