You shouldn't be rephrasing "unless" using "implies". Instead, simply replace it with "or", and it works:
EITHER the correctness of a computer program is established
OR no amount of testing can show that it produces the desired output for all input values
OR every input value is tested
(The "either" and "or" here are inclusive.)
By the way, Rosen's "Discrete Mathematics" textbook has severe conceptual flaws and is very likely to impede mathematical understanding unless you are already mathematically trained or inclined.