1. The problem statement, all variables and given/known data Suppose I want to prove the following statement by contradiction: [itex] P \longrightarrow (Q \land Z) [/itex] 2. Relevant equations If [itex] (Q \land Z) [/itex] is false, then either: (i) Q is false and Z is true; (ii) Q is true and Z is false; (iii) Q and Z are false. 3. The attempt at a solution Do I need to consider all possible cases in which [itex] (Q \land Z) [/itex] is false and arrive to a contradiction or it suffices to show a contradiction in only one possible of the three possible cases? Thanks for your help!