Jitpro Exercise 1.1

Prove Peirce's Law: ((p → q) → p) → p

Jitpro Exercise 1.2

Determine if each proposition is valid or not. If the proposition is not valid, then find a logical interpretation where it is not satisfied.

¬(p → p) → q → p

¬(q → p) → q → p

¬(p → q) → q → p

Jitpro Exercise 1.3

Determine if each proposition is valid or not. If the proposition is not valid, then find a logical interpretation where it is not satisfied.

(p → q) ∨ (q → p)

(p → r) → (p ∧ r → q) → (r → q)

(p → q) → (p ∧ r → q) → (r → q)

(r → p) → (p ∧ r → q) → (r → q)

Jitpro Exercise 1.4

(p → q) = (¬ p ∨ q)

(p → q) = (¬ q → ¬ p)

Jitpro Exercise 1.5

(p = q) = ((¬ p) ≠ q)