Homework for Philosophy 270, Fall 2006

Answer to homework on §2.2

Construct a derivation to show: A ∧ B, (C ∧ D) ∧ E ⇒ C ∧ (B ∧ D).

(Notice that this is the same as showing that the argument

A ∧ B
(C ∧ D) ∧ E
C ∧ (B ∧ D)

is valid. That means that your derivation should begin with the resources A ∧ B and (C ∧ D) ∧ E on separate lines.)

off 0 1 2 3 4 5 6 7 8 on
│A ∧ B 1
│(C ∧ D) ∧ E 2
├─
1 Ext │A (8)
1 Ext │B (7)
2 Ext │C ∧ D 3
2 Ext │E
3 Ext │C (5)
3 Ext │D
│
││●
│├─
5 QED ││C 4
│
│││●
││├─
7 QED │││B 6
││
│││●
││├─
8 QED │││D 6
│├─
6 Cnj ││B ∧ D 4
├─
4 Cnj │C ∧ (B ∧ D)
Proximate arguments of the gaps at each stage
A ∧ B, (C ∧ D) ∧ E / C ∧ (B ∧ D)
A, B, (C ∧ D) ∧ E / C ∧ (B ∧ D)
A, B, C ∧ D, E / C ∧ (B ∧ D)
A, B, C, D, E / C ∧ (B ∧ D)
A, B, C, D, E / C A, B, C, D, E / B ∧ D
● A, B, C, D, E / B A, B, C, D, E / D
● ●