Question

13. Natural Deduction Practice 9 Aa Aa As you learn additional natural deduction rules, and as the proofs you will need to complete become more complex, it is important that you develop your ability to think several steps ahead to determine what intermediate steps will be necessary to reach the argument's conclusion Completing complex natural deduction proofs requires the ability to recognize basic argument patterns in groups of compound statements and often requires that you "reason backwards" from the conclusion to identify what rules will allow you to obtain the conclusion 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 Complete the following natural deduction proof. The given numbered lines are the argument's premises, and the line beginning with a single slash is the argument's conclusion. Derive the argument's conclusion in a series of new lines using the proof checker below. Click Add Line to add a new line to your proof. Each new line must contain a propositional logic statement, the previous line number(s) from which the new statement follows, and the abbreviation for the rule used. As long as every step is correct and you successfully obtain the argument's conclusion on its own line, the proof is correct. You may use any of the eight rules of implication in your proof. In some cases, there may be more than one correct path you can take to reach the conclusion. You can check each line as you go, or you can wait until your proof is completed to check the entire proof. If you make a mistake, click the line you would like to modify. Note: You may need to recheck subsequent lines if you make a change to an already-entered line. When you have completed your proof, click Check Proof. 2 FVG Add Line

Answer 1

please comment if you have any further concern.

Steps Reason Premise Premise Premise 3. G 2, 3, DS 4. F 1, Simp 5. (FoG) 6. G 4, 5, MP 3, 6, Contradictory premises Both G and G can't be true. So, it means that at least one of the premises is false. so, the argument is always valid irrespective of what the conclusion is.