Question

The statement p → (q → p) is equivalent to ______.

Options

• p → (p → q) 

• p → (p ∨ q) 

• p → (p ∧ q) 

• p → (p ↔ q)

Answer 1

The statement p → (q → p) is equivalent to p → (p ∨ q).

Explanation:

p → (q → p) 

= p → (∼ q ∨ p)    ...(Implication equivalence)

= ∼ p v (∼ q ∨ p)   

= (∼ p ∨ p) ∨ ∼ q   ...(Associative law)

= T ∨ ∼ q  ...(Complement law)

= T

Also p → (p ∨ q)  = ∼ p v (p ∨ q)

= (∼ p ∨ p) ∨ q

= T ∨ q

= T