Chapter 11a: One Sided Truth Trees
1.(b)Note that premise one is superfluous. Section 12.1 sheds light on this matter.-(C & D) open
-(C v D) --- -C -D / \ -C -D 2.(b)
W -> D -W
--D --- D / \ -W D 3.(b)
B -> W
-B -> A
-(W v A) --- -W -A / \ -B W / \ * --B A * * 5.(b) R v -R valid
R -> (F & S)
-R -> -(F v S)
--(F & -S) ---
F & -S F -S / \ -R
F & S / \ F --R
-(F v S) S * -F * -S *
7. -B valid
B v M
-M
---
/ \
B M
* *
11. -W invalid
--{[(W & K) & P] -> E}
---
[(W & K) & P] -> E
/ \
-[(W & K) & P] E
/ \
-(W & K) -P
/ \
-W -K
The double conjunction in the conclusion may be grouped
differently.Tree construction can stop after the first right branch is complete.
12.(b)P <-> W valid
-(P & W)
--(P v W) ---
P v W / \ P -P W -W / \ / \ -P -W -P -W * * / \ / \ P W P W * * * *