Exercise 6.5 (Rules). Explain the following rules in natural language:

1 x ∨ x is a tautology – Law of the excluded middle;

2 x ∨ (y ∨ z) → (x ∨ y) ∨ z – Associative rule;

3 x → (x ∨ y) – Expansion rule;

4 (x ∨ x) → x – Contraction rule;

5 (x ∨ y) ∧ (x ∨ z) → (y ∨ z).