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5) Jones, Smith, and Clark hold the jobs of programmer,knowledge engineer, and manager (not necessarily in that order). Jones owes the programmer$10. The manager's spouse prohibits borrowing money. Smith is not married. Your task is tofigure out which person has which job.Represent the facts in prepositional logic. You should have nine propositional symbols torepresent the possible person/job assignments. Solve the problem by showing thatonly one of them is implied by KB, and by saying what its interpretation is.

Question

  1. Jones, Smith, and Clark hold the jobs of programmer,knowledge engineer, and manager (not necessarily in that order). Jones owes the programmer$10. The manager's spouse prohibits borrowing money. Smith is not married. Your task is tofigure out which person has which job.Represent the facts in prepositional logic. You should have nine propositional symbols torepresent the possible person/job assignments. Solve the problem by showing thatonly one of them is implied by KB, and by saying what its interpretation is.
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Solution

Let's represent the facts in prepositional logic:

P: Jones is the programmer. K: Smith is the knowledge engineer. M: Clark is the manager.

Now, let's represent the given information using these propositional symbols:

  1. Jones owes the programmer 10.ThiscanberepresentedasP(JowesP10. This can be represented as P ∧ (J owes P 10).

  2. The manager's spouse prohibits borrowing money. This can be represented as M → ¬(M owes X $10), where X represents any person.

  3. Smith is not married. This can be represented as ¬(S owes X $10), where X represents any person.

Now, let's analyze the given information step by step:

  1. Jones owes the programmer $10. This implies that Jones is the programmer. Therefore, we can infer P.

  2. The manager's spouse prohibits borrowing money. Since Smith is not married, this rule does not apply to him. Therefore, we cannot infer anything about the manager or the knowledge engineer.

  3. Smith is not married. This implies that Smith cannot be the manager or the knowledge engineer. Therefore, we can infer ¬M and ¬K.

Based on the given information and the inferences made, we can conclude that Jones is the programmer (P), Smith is not the manager (¬M), and Smith is not the knowledge engineer (¬K).

This problem has been solved

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