Truth Tellers & Liars

1. Represent statements in logic form.

   • X is lying → ¬T(X)
   • X and Y are telling the truth → T(X) ∧ T(Y)

2. Assign variables:

   • T(P) = P tells the truth
   • ¬T(P) = P lies

3. Test cases:
   • Assume one person is a truth-teller, check for consistency.
   • Assume one person is a liar, check for contradictions.
4. Eliminate contradictions until only one consistent assignment remains.

• A says: "B is lying."
• B says: "A and I are telling the truth."

Case 1: A = truth-teller → B = liar → B’s statement false → consistent. Case 2: A = liar → B = truth-teller → contradiction.

→ Solution: A = truth-teller, B = liar.