Step 1: Understanding the Question:
The question asks to classify a logical expression based on its truth table.
A Tautology is always True, a Contradiction is always False, and a Contingency is a mix of both.
Step 2: Key Formula or Approach:
Use a Truth Table to evaluate all possible combinations of truth values for \( p \), \( q \), and \( r \).
The implication \( X \to Y \) is false only when \( X \) is True and \( Y \) is False.
Step 3: Detailed Explanation:
We evaluate the expression \( (p \land \sim q) \to r \):
1. If \( p=T, q=F, r=F \):
\( \sim q = T \).
\( (p \land \sim q) = (T \land T) = T \).
\( T \to F = F \).
2. If \( p=T, q=T, r=T \):
\( \sim q = F \).
\( (p \land \sim q) = (T \land F) = F \).
\( F \to T = T \).
Since we found at least one case where the statement is False and at least one case where it is True, the statement is neither a tautology nor a contradiction.
Step 4: Final Answer:
The statement pattern is a Contingency.