6. (5+5 points) (a) Show that for all 4, 4, 0, x = S(P), each of the following holds: (i) 4, (x⇒ 4) = v; (ii) If, then ¬¬; and 0 = x, then (^0) = (& ^ x); (iii) If (iv) If and 0=x, then ( V ) = ( & V x ); (v) If and = 0, then ( √ √) = 0. (b) Let ACS(P) and let Є S(P). Show that if A, 41, then A¬.