only part (b)

6. (5+5 points) (a) Show that for all 4, 0, 0, X E S(P), each of the following holds: (i) 4,( 40) ; (ii) If YFX, then 2 FG; (iii) If FW and 0 F X, then (410) F ( ^x); (iv) If = x and 0 = x, then (VO) E (V x); (v) If 6 = 0 and = 0, then (4 V %) = D. (b) Let A CS(P) and let v S(P). Show that if A, F1, then AF