Now here's some more theorems that definitely need DML!
I mean, they're obviously true, but how to prove them? Well, here's the first one.
1.
2.
3.
4.
5. 6. 7. 8. 9. 10. 11. 12.
Show
P v (Q v R) (P v Q) v R
P v (Q v R)
Show
(P v Q) v R
~ [(P v Q) v R]
~ (P v Q) ^ ~ R
~ (P v Q)
~ P ^ ~Q
~ P
Q v R
~Q
R
~ R
CP
ACP
IP
AIP
4, DML
5, S 6, DML
7, S
2, 8, DS
7, S
9, 10, DS
5, S
Can you figure out how to prove the other three? Well number 12 should be about the same as number 11, but what about numbers 13 and 14?
Actually, numbers 13 and 14 are incredibly easy! Think about it. If you have trouble with them, see the hint at the bottom of this page.
For practice, and to prepare for the quiz, here are some arguments. Identify and cross out the invalid ones. circle and derive the valid ones. (Use the truth table method to determine validity, if needed.)