Final answer:
The statement is true because a set of tautologies, which are always true, cannot contain contradictions and therefore such a set would indeed be consistent.
Step-by-step explanation:
If all the members of a set of formulas are tautologies, then the set must be consistent. The correct answer is A. True. A tautology is a formula that is true under every interpretation, and if every formula in a set is a tautology, that means every formula is always true. Hence, there can be no contradiction among them, which implies that the set is consistent.
Defining the concept of consistency in the context of logical statements, a set of beliefs or statements is considered consistent if it is possible for them to all be true at the same time. Since tautologies are always true, a set comprising only tautologies certainly fulfills this condition. Consistency is key in logical systems and mathematical reasoning; without consistency, a set of statements or formulas can lead to contradictory conclusions, which is an undesirable outcome in logical analysis and proof.