MATH145 Lecture Notes - Lecture 13: F 17 Kallinge

• School: University of Waterloo
• Department: Mathematics
• Course: MATH145
• Professor: Stephen New

Document Summary

{f (g h), (f g) h} (cid:15) h. Suppose h is false (f g) h, h f g (f g) f. Here is a derivation for the valid argument. S = {f (g h), (f g) h, h} (cid:15) f (g h) {f (g h), (f g) h} (cid:15) h by v1 by v1. V23 on line 1,5 by v12 on 6. Suppose that f (g h) is true (under ) Suppose that (f g) h is true. Note that wither f g is true or h is true. Since f (g h) and f f [v23] In either case, we have proven h [v14] Solution: we need to show that for every assignment if (f g) h is true under and f (g h) is true then h f is false. Suppose (f g) h is true. Suppose f (g h) is true. [we need to show that h f is false.