Determine whether the following compound statement is a tautology or contradiction.(p → (q → r)) → ((p ∧ q ) → r)

To determine whether the compound statement is a tautology or contradiction, we can use the truth table method. Here are the steps:

1. Identify the individual statements: In this case, we have three individual statements p, q, and r.

2. Create a truth table: The truth table should have a column for each individual statement and a column for each part of the compound statement. Since we have three individual statements, we will have 2^3 = 8 rows in our truth table.

3. Fill in the truth values: Start by alternating T (true) and F (false) in the p column, then two Ts and two Fs in the q column, and then four Ts and four Fs in the r column.

4. Calculate the truth values for the compound statements:

   • For p → (q → r), the result is F only when p is T and (q → r) is F. In all other cases, the result is T.

   • For (p ∧ q ) → r, the result is F only when (p ∧ q) is T and r is F. In all other cases, the result is T.

5. Compare the final columns: If all the values in the final column are T, then the compound statement is a tautology. If all the values are F, then it's a contradiction. If there's a mix of T and F, then it's neither a tautology nor a contradiction.

By following these steps, you can determine whether the compound statement is a tautology, contradiction, or neither.