Decide whether each of the following sentences is valid, un-satisfiable, or neither. Verify your decisions using truth tables or the equivalence rules of Figure.

a. Smoke ↔ Smoke

b. Smoke → Fire

c. (Smoke → Fire) → (—Smoke → –––Fire)

d. Smoke V Fire V —Fire

e. ((Smoke Λ Heat) → Fire) ↔ ((Smoke → Fire) V (Heat → Fire))

f. (Smoke → Fire) → ((Smoke Λ heat) → Fire)

g. Big V Dumb V (Big → Dumb)

h. (Big Λ Dumb) V ––Dumb