Context: Here is a model: Domain: {1, 2, 3, 4} B : {3, 4}, C : {1, 4}, F : ∅ Make a proposition that is false in this model by filling in each of the blank spaces of （blank)z((B（blank)（blank) z) →（blank)（blank)y¬F y) with one symbol of MPL. Explain why the proposition you made is false in the given model. Answer question
Question
Context: Here is a model: Domain: {1, 2, 3, 4} B : {3, 4}, C : {1, 4}, F : ∅ Make a proposition that is false in this model by filling in each of the blank spaces of （blank)z((B（blank)（blank) z) →（blank)（blank)y¬F y) with one symbol of MPL. Explain why the proposition you made is false in the given model. Answer question
Solution
Sure, let's fill in the blanks with the symbols of MPL (Modal Propositional Logic) to create a proposition that is false in the given model.
Let's fill in the blanks as follows:
∀z((Bz ∧ ∃z) → ∃y¬Fy)
This proposition can be read as: "For all z, if z is in B and there exists such a z, then there exists a y such that y is not in F."
Now, let's see why this proposition is false in the given model.
In the given model, B includes {3, 4} and F is an empty set. According to the proposition, if a number is in B, then there should exist a number that is not in F. However, since F is an empty set, every number is not in F. Therefore, the proposition should be true for all numbers in B, which are 3 and 4.
However, the proposition is a universal statement, meaning it should hold true for all elements in the domain. The domain in the given model is {1, 2, 3, 4}. For the numbers 1 and 2, which are not in B, the proposition does not hold true because the implication "if z is in B then there exists a y such that y is not in F" is not satisfied. Therefore, the proposition is false in the given model.
Similar Questions
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