Final answer:
The conclusion that can be drawn from the given logical statements is that they are logically equivalent. This is a disjunctive syllogism, and therefore, the correct option is 'the statements are logically equivalent'. A and B both are logically correct.
Step-by-step explanation:
The question given is related to logical equivalency between two statements. When evaluating the logic, we translate the initial statement into formal logic as "Not (P and Q)" which implies "Not P or Not Q". So, when being told 'It is not the case that you studied for your test and passed it', this logically means 'You did not study for your test or you did not pass it'. This is known as a disjunctive syllogism in logic, and thus, the statements given are indeed logically equivalent.
The initial logic can be seen as a denial of a conjunction, which in logic, is equivalent to the assertion of a disjunction. Hence, these types of statements are reflective of conditional reasoning where the conditions are set by the relations of necessity and sufficiency. If the first statement is true, it necessitates that at least one of the components - not studying or not passing - is true, thus affirming the second statement.
Therefore, the conclusion that can be confidently drawn is that statements A and B are logically equivalent, which corresponds to option C: 'the statements are logically equivalent'. When you mentioned correct option in final answer, this assures the precision of your result in logical analysis.