Derivation Exercises for Unit 3 Part 1:
Derivations with Conditional and Negation
© Niko Scharer
1
Derivations Exercises Unit 3 Part 1
Derivations with NEGATION and CONDITIONAL
SELECTED ANSWERS QUESTIONS 20-70
Answers only for selected derivations.
In the annotations:
conc= conclusion, ant= antecedent, cons=consequent, cond=conditional
Use any derivation method (DD, CD, ID) and any rule (MP, MT, DN and R).
20.
R
→
~ R .
∴
~R
1 Show
~R
show conc
2
R
ass id
you can’t show ~R directly, so assume the opposite
goal:
a contradiction
3
~R
pr1 2 mp
use your assumption!
4
2 3 id
lines 2 and 3 contradict each other.
The indirect
derivation is complete.
Box and cancel.
21.
P
→
Q.
~P
→
Q.
∴
Q
1 Show
Q
show conc
2
~Q
ass id
you can’t show Q directly, so assume the opposite
goal:
a contradiction
3
~P
2 pr1 mt
use your assumption!
4
~~P
2 pr2 mt
use your assumption again!
5
3 4 id
lines 3 and 4 contradict each other.
ID is done.
Box and cancel.
24.
~~R
→
~~T .
∴
~T
→
~R
1 Show
~T
→
~R
show conc
2
~T
ass cd
assume the ant. of 1; goal:
cons. of 1: ~R
3
~~~T
2 dn
4
~~~R
3 mt
5
~R
4 dn cd
derived cons. of 1.
CD done.
Box & cancel

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*