2.2.x. Exercise questions

1. 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.]
e. A ∧ (B ∧ C) ⇒ (B ∧ A) ∧ (C ∧ A)

For more exercises, use the exercise machine.

Glen Helman 28 Aug 2008