I only know the old way to do indirect proofs.
The modern way may be different, although the
thinking process must be the same. Maybe you can
translate my old way into your new way, and maybe
even teach me something about the modern way for
indirect proofs in the thank-you note form below.
I would appreciate it.
Doing it the old way, we reach a contradiction
t > f in statement 16.
Assume the premises are true, and the conclusion is false.
So we have this:
1. B v R is true
2. (R v D) > J is true
3. ~J > ~(B v A) is true
4. J is false
5. ~f>~(B v A) is true 3,4, replacing J by f
6. t>~(B v A) is true 5, replacing ~f with t
7. ~(B v A) is true 6, the only way 6 can be true
8. B v A is false 7, the negation is true
9. B is false; A is false 8, the only way B v A can be false
10. f v R is true 1,9, replacing B by f
11. R is true 10, the only way f v R can be true
12. (f v D) > f is true 2,4,11, replacing R and J by f
13. f v D is false 13, the only way 12 can be true
14. D is false 13, the only way f v D can be false
15. R v D is true 11,14, R is true and D is false
16. t > f is true (contradiction) 2,15,4, replacing (R v D) by t, J by f
Edwin
