Consider the functions Div and Mod such that Div(x, y) and Mod(x, y) compute the quotient and remainder, respectively, of the division of x by y. These are not total functions because division by 0 is...

Consider the functions Div and Mod such that Div(x, y) and Mod(x, y)

compute the quotient and remainder, respectively, of the division of x by y.

These are not total functions because division by 0 is not defined, but we

can complete the definition by stating that Div(x, 0) = 0 and Mod(x, 0) =

x. Show that the extended functions Div and Mod are primitive recursive.