Logic Proof With Rules of Replacement

In summary, the conversation discusses the relationship between workers' fundamental right to a job and the potential consequences for unemployment and job security. Based on the given symbols and rules, it is possible to conclude that either unemployment will be virtually nonexistent or production efficiency will be maximized.
  • #1
MRF2
4
0
Not sure if this is an allowed post, as it is not technically math but I'm trying to work through the below proof.

If workers have a fundamental right to a job, then unemployment will be virtually nonexistent but job redundancy will become a problem. If workers have no fundamental right to a job, then production efficiency will be maximized but job security will be jeopardized. Workers either have or do not have a fundamental right to a job. Therefore, either unemployment will be virtually nonexistent or production efficiency will be maximized. (F, U, R, P, S)

I have it symbolized as
1) F > (U•R) given
2) ~F > (P•S) given
3) F v ~F // U v P given
4) [F > (U • R)] • [~F > (P•S)] Conj. 1,2
5) (U • R) v (P • S) CD 3,4

but have gotten stuck at line 5. I am allowed to use all the rules of inference and the following rules of replacement: de morgans, commutation, association, distribution, double negation.

Thank you!
 
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  • #2
MRF2 said:
I am allowed to use all the rules of inference
See this thread.
 

FAQ: Logic Proof With Rules of Replacement

1. What are the basic rules of replacement in logic proofs?

The basic rules of replacement in logic proofs are Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunctive Syllogism, Constructive Dilemma, Destructive Dilemma, Conjunction, Simplification, Addition, and Double Negation.

2. How do you use the rules of replacement in a logic proof?

To use the rules of replacement in a logic proof, you must first identify the premises and conclusion of the argument. Then, you can apply the appropriate rule of replacement to each step in the proof, making sure to follow the correct order of operations.

3. Can you combine multiple rules of replacement in a single step of a logic proof?

Yes, it is possible to combine multiple rules of replacement in a single step of a logic proof. This is known as a compound rule of replacement and can be used to simplify the proof and make it more efficient.

4. What is the purpose of using rules of replacement in logic proofs?

The purpose of using rules of replacement in logic proofs is to demonstrate the validity of an argument by breaking it down into smaller, simpler steps. By applying these rules, we can show that the conclusion logically follows from the premises, providing a sound and convincing argument.

5. Are there any limitations to using rules of replacement in logic proofs?

While rules of replacement are a powerful tool in logic proofs, they do have some limitations. They can only be used in propositional logic, which means they cannot be applied to arguments that involve quantifiers or other forms of logic. Additionally, they can only be used to prove validity, not soundness, of an argument.

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