let IF be an ordered field, not necessarily complete. prove or disprove the following claims: a) A = A.A (AB = {a.blae A, be B} b) if A is bounded above set, then A is also bounded above. c) if A is bounded, then A is also bounded. d) if s = max (A) is exists and A\ {s} & then + S = sup (A\ {s}). e) if s= sup (A) exists and SEA then s= max(A). f) if s = sup (A) exists and 5&A then max (A) is not existing.