Prove the following theorem formally and in detail. Number each of your statemen

Question

Prove the following theorem formally and in detail. Number each of your statements. For your justifications you may use tautologies.

[rs, tu,st]ru

Explanation / Answer

So I might have different names then you do, however heres a decent outline: 1. s -> ~r given 2. t -> u given 3. s or t given 4. ~s or ~r def of material conditional (ie def of ->) from 1 5. Disjunction elimination on ~s or ~r 6. assume ~s 7. t disjunctive syllogism with 3 and 6 8. u modus ponens with 7and 2 9. u or ~r disjunctive introduction with 8 10.assume ~r 11. u or ~r disjunctive introduction with 10. 12. u or ~r by disjunctive elimination( with 5 - 11) I tried to use indenting to show you where you would align the indents for nice formatting. I think you might be able to do it without disjunction elimination, but this way was the first I thought of so I went with it, hope it helps and let me know if something doesn't make sense / you can't use it as a law yet.

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