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QUESTION 3 Consider the arguments below and decide whether they are valid. If they are, write down an informal proof, phrased in complete, well-formed English sentences. If the argument is invalid, construct a counter example. In Questions 3.1 and 3.3 we assume we deal with the blocks language. Question 3.1 | x or y is at home but either v or z is unhappy | Either x is not home or z is happy. | Either y is not home or z is unhappy |--- | z is unhappy Question 3.2 | Aggie or Cecil is not shopping. | Cecil is shopping or Cecil and Aggie are married. | Aggie and Cecil are not married or Aggie is shopping. |---- | Cecil and Aggie are married. Question 3.3 | Student(peter) ∨ Hungry(peter, 2:00) | ¬ Hungry(peter, 2:00) ∨ ¬Pet(patience) | Pet(patience) ∨ ¬ Student(peter) |---- | Student(peter)
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