A tautology is a logical statement or formula that is always true, regardless of the truth values of its components. In other words, it is a statement that is true in every possible interpretation.
If a statement is a tautology, it means that it is logically true and cannot be false. This is because its truth value is determined solely by its logical form and not by the truth values of its components.
To prove that a statement is a tautology, you can use logical equivalences or truth tables to show that the statement is always true, regardless of the truth values of its components.
The statement being asked about is (\neg B \wedge (A \Rightarrow B)) \Rightarrow \neg A. This is a conditional statement, which means that it only holds true if the antecedent (\neg B \wedge (A \Rightarrow B)) is true and the consequent (\neg A) is also true.
Determining if a statement is a tautology is important because it helps us understand the logical relationships between different statements and can be used to simplify complex logical expressions. It also allows us to identify valid arguments and avoid logical fallacies.