Final answer:
The statement 'All Java programs have at least 5 lines' is accurately translated to '∀ x, if Java programs have less than 5 lines, then they are invalid.', following deductive reasoning principles.
Step-by-step explanation:
The correct way to rewrite the statement "All Java programs have at least 5 lines" in the form "∀ _____ x, if _____ then _____" would be option a: ∀ x, if Java programs have less than 5 lines, then they are invalid. This follows logical structures within deductive reasoning since we know that a necessary condition for a Java program to be considered valid, based on the initial statement, is that it has at least 5 lines. Thus, a program with less than 5 lines does not meet this criterion and is therefore considered invalid.
The correct option to rewrite the statement in the form '∀ _____ x, if _____ then _____' is option c: ∀ x, if Java programs have at least 5 lines, then they are valid.
In this form, the statement says that for all Java programs, if they have at least 5 lines, then they are valid.
For example, if we have a Java program with 7 lines of code, then according to this statement, it would be considered valid.