Define the closed binary operation (Exclusive or) on Fn, the set of all Boolean functions on

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

Transcribed Image Text:

fe 8) = feg= feg