Question

Prove that for any propositions p,q,r the compound proposition {pà ƒ ƒ ¢ † ’(qà ƒ ƒ ¢ † ’r)}à ƒ ƒ ¢ † ’{(pà ƒ ƒ ¢ † ’q)à ƒ ƒ ¢ † ’(pà ƒ ƒ ¢ † ’r)} is a tautology

Answer 1

Solution:

Assume given compound proposition is:

$((p → q) ∧ (q → r)) → (p → r)$

Truth table:

Thus, it is a tautology.