MHB Logic Proof With Rules of Replacement

AI Thread Summary
The discussion revolves around a logical proof concerning workers' rights and its implications on unemployment and production efficiency. The proof asserts that if workers have a fundamental right to a job, unemployment will be low, but job redundancy will increase; conversely, if they lack this right, production efficiency will improve at the cost of job security. The user has formulated the proof using symbolic logic but encounters difficulty at line 5. They are permitted to utilize various rules of inference and specific rules of replacement to advance their proof. The conversation seeks assistance in resolving the logical challenge presented.
MRF2
Messages
4
Reaction score
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!
 
Physics news on Phys.org
MRF2 said:
I am allowed to use all the rules of inference
See this thread.
 
Back
Top