Final answer:
The statements given create a paradoxical situation and cannot be consistently assigned a true or false value.
Step-by-step explanation:
The statements given create a paradoxical situation. Let's examine each statement:
The first statement says 'The next statement is false.' If this statement is true, then the next statement must be false. However, if the next statement is false, then the first statement would be true, leading to a contradiction.
The second statement says 'The next statement is true.' If this statement is true, then the next statement must be true. However, if the next statement is true, then the first statement would be false, again leading to a contradiction.
The third statement says 'The two previous statements are false.' This statement cannot be true because at least one of the previous statements must be true for the third statement to exist.
Therefore, these statements create a paradox and cannot be consistently assigned a true or false value. So, the answer is indeterminate or undefined.