2.4.xa. Exercise answers

The answers below avoid the use of Cnj in order to maximize the use of the rule Adj. In some cases, a mixed use of the two would have produced a more natural argument.

1.
│A (1)
├─
1 Adj │A ∧ A X,(2)
│●
├─
2 QED │A ∧ A
2.
│A ∧ B 1
│B ∧ C 2
│B ∧ D 3
├─
1 Ext │A (4)
1 Ext │B
2 Ext │B
2 Ext │C
3 Ext │B
3 Ext │D (4)
4 Adj │A ∧ D X,(5)
│●
├─
5 QED │A ∧ D
3.
│A ∧ B 1
├─
1 Ext │A (2),(3)
1 Ext │B (2)
2 Adj │B ∧ A X,(3)
3 Adj │A ∧ (B ∧ A) X,(4)
│●
├─
4 QED │A ∧ (B ∧ A)
4.
│A (2)
│B ∧ C 1
│D
├─
1 Ext │B (2),(4)
1 Ext │C (3)
2 Adj │B ∧ A X,(3)
3 Adj │C ∧ (B ∧ A) X,(4)
4 Adj │(C ∧ (B ∧ A)) ∧ B X,(5)
│●
├─
5 QED │(C ∧ (B ∧ A)) ∧ B
5.
│A ∧ B 1
├─
1 Ext │A (2),(3)
1 Ext │B (2)
2 Adj │B ∧ A X,(3),(4)
3 Adj │A ∧ (B ∧ A) X,(4)
4 Adj │(B ∧ A) ∧ (A ∧ (B ∧ A)) X,(5)
│●
├─
5 QED │(B ∧ A) ∧ (A ∧ (B ∧ A))
Glen Helman 01 Aug 2004