Final answer:
The statement that a set of formulas containing a contradiction must be inconsistent is true. Contradictions imply that not all statements in the set can be true at the same time, thus leading to inconsistency.
Step-by-step explanation:
If a set of formulas contains a contradiction, then the set must be inconsistent. The answer to this question is A. True. According to principles of logical consistency, a contradiction occurs when a statement and its negation are both present in the same set, implying that at least one statement in the set must be false. This incoherence deems the set inconsistent because it's impossible for contradictory statements to be true simultaneously.
For example, if a set includes the statements 'All birds can fly' and 'Some birds cannot fly,' these statements contradict each other, rendering the set inconsistent. To maintain consistency, a philosopher or logician would need to modify the beliefs or discard some in order to resolve the contradiction.