Final answer:
The domain of the function F(x) = logob^x consists solely of positive real numbers, which makes the statement True.
Step-by-step explanation:
The statement that the domain of F(x) = logob^x is the set of all positive real numbers is A) True. In mathematics, the domain of a logarithmic function is indeed all positive real numbers because the logarithm of a number is only defined for positive entries. This is due to the properties of logarithms and exponential functions, where the base of a logarithm (in this case, b) must be a positive number other than 1, and the input of the logarithmic function (x) must be a positive number as well to produce a real result. Hence, F(x) = logob^x can only accept positive real numbers as valid inputs.