Define the closed binary operation (Exclusive or) on Fn, the set of all Boolean functions on n variables, by f g = f

Define the closed binary operation Š• (Exclusive or) on Fn, the set of all Boolean functions on n variables, by f Š• g = f + g, where f, g: Bn †’ B.
(a) Determine f Š• f, f Š• , f Š• 1, and f Š• 0.
(b) Prove or disprove each of the following.
(i) f Š• g = 0 ‡’ f = g
(ii) f Š• (g Š• h) = (f Š• g) Š• h
(iii) f Š• g = Š•
(iv) f Š• gh = (f Š• g)(f Š• h)
(v) f(g Š• h) = fg Š• fh

(vii) f Š• g = f Š• h ‡’ g = h

fe 8) = feg= feg