Final answer:
The statement that tautologies are only entailed by other tautologies is false because a tautology, which is true by definition in any scenario, can be entailed by any statement, tautological or not, as long as it is true.
Step-by-step explanation:
The statement that tautologies are only entailed by other tautologies is false. In logic, a tautology is a formula that is true in every possible interpretation. However, a tautology can be entailed by any statement because if the premises of an argument are true, then the conclusion (which may be a tautology) must also be true. For instance, any premise, whether it's a tautology or not, will entail the tautology 'A or not A' because this is always true.
An example of a non-tautological premise that entails a tautology is the statement 'The sun is a star'. This statement is not a tautology because it could be false in another possible world where 'sun' refers to something that isn't a star. However, it does entail the tautology 'Either the sun is a star, or it is not a star' because the latter statement is true regardless of the truth of the first statement.