I've been trying to do the following two proofs for over 2 days and haven't gotten anywhere. Can someone help me? These proofs can be done using all the rules of inference and rules of replacement and also conditional and indirect proofs.
I'm not going to write the names of the rules of inference because those vary by professor. Hopefully it'll be obvious. All of the steps I take involve basic rules of inference
1.)
Premises:
(A > I) > (C>D)
(A >~I) > (Y>Z)
Using these 2 premises, prove that: (C>D) v (Y>Z)
1. (A > I) > (C>D)
2. (A >~I) > (Y>Z)
3. ~(A > I) v (C>D) from 1
4. ~(A >~I) v (Y>Z) from 2
5. ~(~A v I) v (C>D) from 3
6. (A & ~I) v (C>D) from 5 (this is demorgan's law)
7. ~(~A v ~I) v (Y>Z) from 4
8. (A & I) v (Y>Z) from 7 (demorgan's law again)
9. Now suppose ~[(C>D) v (Y>Z)] for proof by contradiction
10. ~(C>D) & ~(Y>Z) from 9 (demorgan)
11. ~(C>D) from 10
12. A & ~I from 11 and 6
13. ~I from 12
14. ~(Y>Z) from 10
15. A & I from 14 and 8
16. I from 15
17. I & ~I from 13 and 16 that's the end of the proof by contradiction soooo
18. (C>D) v (Y>Z)
TADA
I was going to do the second for you too but the first took forever to write out and I don't want to spend any more time on this. Maybe the demonstration of this one will help you figure out the other.
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