Let S denote the set of positive real numbers. Define operations and by the equations and x + y := xy xoy :=xlny (a) Prove that S with the operations and is a ring. What are 0s and 1s? (b) Is S commutative? (c) Find the units and the zero divisors in S. For every unit u € S, find its inverse v, i.e., v € S such that u Ov=vOu=1s.

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