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Define an if - then - else construct as a primitive recursive function, i.e. given two functions f.g, an argument r, and a boolean expression e, the if -then - else construct should apply f or g to r depending on the boolean value of e. You don't have to use the same strict way to define a primitive recursive function as long as you are able to justify the correctness of your definitions. Example you can define a recursive definition of addition like +(r, 0) Prime test: if r ENthen prime(x otherwise. if is a prime number and prime(x) 0