As you learn additional natural deduction rules, and as the proofs you will need to complete become more complex, it is important that you device your ability to think several steps ahead to determine what intermediate steps will be necessary to reach the argument's condition. Completing complex natural deduction proofs requires the ability to recognize basic argument patterns in groups of compound statements and often requires that you "reason backward" from the conclusion to identify what rules will allow you to obtain the condusion and in what order they must be applied Developing these skills requires regular practice and repetition completing increasingly complex proofs. You are allowed to try three different versions of each page in this problem set. Even if you find a proof on one page to be easy, it is a good idea to try the other versions of each page to get as much practice completing proofs as possible. Consider the natural deduction proof given below. Using your knowledge of the natural deduction proof method and the options provided in the drop-down menus, fill in the blanks to identify the missing information (premises, inferences, or justifications) that completes the proof. Remember: The conclusion statement should appear twice in your completed proof.
1. ~T.(FEM)
2. (~TvC) (j•~W)
3 ~T
4. ~TvC Add
5 2,4 MP
6 J 5 Simp
7 3,6 conj