# Logic Proof With Rules of Replacement

• MHB
• MRF2

#### MRF2

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!

MRF2 said:
I am allowed to use all the rules of inference