1) The inverse [P(Rf), P(Df), f] is always a single-valued function. Show that f is a single-valued function. 2) Find the inverse image of (1/2, 4] under 1(1,2]. 3) Is the set of all continuous real-valued functions a lattice? 4) Is the set of all real-valued polynomials a lattice? 5) Prove that ??× ??! = (??×??!) !?! !?! 6) Let ??!,…, ??! ? ??! ?????? ??!,…, ??! ? ??!. Show that [ ??!]×[ ??!] = (??!×??!) ! !!! ! !!! ! !!! ! !!!