Restate the derivation below as a tree-form proof, labeling each horizontal line with the number of the stage at which it is entered. That is, do what is done with the example in 2.2.4
│(A ∧ C) ∧ B
1
├─
1 Ext
│A ∧ C
2
1 Ext
│B
(4)
2 Ext
│A
2 Ext
│C
(5)
│
││●
│├─
4 QED
││B
3
│
││●
│├─
5 QED
││C
3
├─
3 Cnj
│B ∧ C
2.
Use the system of derivations to establish each of the following claims of entailment:
a.
A ∧ B ⇒ B ∧ A
b.
A ⇒ A ∧ A
c.
A ∧ (B ∧ C) ⇒ (C ∧ B) ∧ A
d.
A, B ∧ C, D ⇒ (C ∧ (B ∧ A)) ∧ B
[The derivation for d will have three premises above the initial horizontal line.]