Suppose F is a set whose elements are functions from F to F. That's all you need to know about F. Let F be a member of F. Suppose that in F we have a function G, such that when G is applied to some input X ? F, it returns F applied to X applied to X, that is: G(X) = F (X(X)). Let D be G(G). Prove that D is a fixed point

From the question, we have G ( x ) = F (x (x ) ) - Now, we define Das D= G CG) -2 ") TO prove D is fixed, point, we need to prove that D ( D ) = D. Most of a plago sol so consider, D (D) = G CG) We have G ( x) = F (xocs). then GCGS= F CGCGS) [.: from @] SO, D (D ) = G CG) D ( D ) = F ( G CG ) ) - We also have . D= G CG) from so , (3) becomes GGG ) = FEGEE) ) D ( D ) = F (D ) - Now, we want to show D( D)= D. so, we have to show that F ( D ) = D so , consider, boxit did it de ( a)a joe F ( D ) = F (GCG ) [: From 0 & @ ] F ( D ) = G (GCG ) ) [: From 0] F ( D ) = D - 5 [: From ] Thus , D CD ) = F ( D ) = D (from @) & 5 .. D is fixed point. 4 Sep 2023, 9:03 am