The truth-tree method

  1. Use the truth-tree method to determine whether the following argument is truth-functionally valid or invalid. If it is invalid, recover a
    truth-value assignment that shows this. (10 marks)
    P1 (J T) J
    P2 (T J) T
    C ⇠J _ ⇠T
  2. Use a truth tree to determine whether the sentence
    ([(C D)&(D E)] & C) & ⇠E
    is truth-functionally true, truth-functionally false or truth functionally
    indeterminate. (10 marks)
  3. Using SD, derive D & ⇠D from {(⇠A & B) (B ⌘ D), B (C & ⇠A),
    ⇠D & B}. (10 marks)
  4. Using SD, demonstrate that (A & C) _ (B & C) follows from
    (A _ B) & C. (10 marks)
  5. Using SD, demonstrate that A [B (A B)] is a theorem. (10

Sample Solution