Two column proof and logic laws

Question

((~d V e) ^ (~d V ~e)) -> f ≡ d V f

Answer 1

d e f ~d ~e ~d or e ~d or ~e first term lhs d or f

T T T F F T F F T T

T T F F F T F F T T

T F T F T F T F T T

T F F F T F T F T T

F T T T F T T T T T

F T F T F T T T F F

F F T T T T T T T T

F F F T T T T T F F

~d v (e and ~e) = (~d v e) and (~d v ~e) distributive

~d v (e and ~e) --> f substitution

(~d v F) -> F absorption

~(~d or F) v F implication property

(d and ~f) v F deMorgan's

d v f and (~f v F) distributive

d v f and T absorption

d v f identity