I came across this problem in 5th edition of REA's GRE CS practice book.

Assume I and II are statements that have well-defined truth values i.e. each statement is either true or false and not both. Then this question on the test can be answered without further information, since there must be a unique correct answer.

A) I and II are both false
B) I is true, II is false
C) I is false, II is true
D) I and II are both true
E) If I is false, II is false

It's obvious that E is definitely not the right answer but how can we prove that one of the above answers is right?