(60 points)

1. (12 pts) Exercise 17 Chapter 2.
2. (6 pts) Exercise 1 Chapter 4.  
3. (6 pts) Exercise 3 Chapter 4.
4. (6 pts) Exercise 18 Chapter 4.
5. (30 pts) Consider a Java interface called Rational that specifies the operations on rational numbers.  Mathematically a rational number is defined as the ratio of two integers, where the denominator cannot be zero.  Common methods or operations for such an interface include:
   • "set()" which sets the numerator and denominator values of "this" Rational
   • "add()" which adds a Rational and "this" Rational and returns a third Rational without changing the value of this Rational
   • "addTo()" which adds a Rational to "this" Rational
   • "divide()" which divides "this" Rational by second Rational and returns a third Rational
   • "equals()" which determines if "this" Rational is equal to the second Rational
   Your tasks are:
   1. Provide a formal specification of the Rational interface with the above five methods.  Define this specification as a Java interface, compile that interface, and submit the java file.
   2. Use Java exceptions to deal with any error situations.
   3. Include as part of this specification the behavior for any constructors of a class that implements this interface.
   Note that this is a specification not an implementation question.