Mathematical Logic

To determine whether the proposition is a tautology, contradiction, or neither, let's analyze it step-by-step using a truth table.

The proposition involves two sub-expressions:

• : This is known as the implication which is equivalent to .
• : This is also an implication which is equivalent to .

We determine the truth values of these sub-expressions for all possible values of :

From the truth table, we can observe:

• When is True, the entire proposition is False.
• When is False, the entire proposition is also False.

Since the final column of the truth table indicates that the proposition is False for all possible truth values of , the proposition is a contradiction. A contradiction is a statement that is always false, regardless of the truth values of its components.

Thus, the correct answer is: the proposition is a contradiction.