Problem 1. (a) The declaration F(0) = 1, F(1) = 1, F(n + 2) = F(n)+F(n+1) is not primitive recursive. Show that F is primitive recursive nonetheless. (b) Show that the function nnth digit of V2 is primitive recursive. (c) Show that the function n-> mth digit of is recursive. (+) Show that it is in fact primitive recursive!) Problem 1. (a) The declaration F(0) = 1, F(1) = 1, F(n + 2) = F(n)+F(n+1) is not primitive recursive. Show that F is primitive recursive nonetheless. (b) Show that the function nnth digit of V2 is primitive recursive. (c) Show that the function n-> mth digit of is recursive. (+) Show that it is in fact primitive recursive!)