Section 7.5: Conditional Proof Graded Assignment Due Tuesday 1314 17 at 01:00 PM

Question

Section 7.5: Conditional Proof Graded Assignment Due Tuesday 1314 17 at 01:00 PM Attempts: Average: 10 5. Conditional Proof Natural Deduction Practice 4 Use the conditional proof method and the eighteen rules of inference to compete the following natural deduction proof. Depending on the argument, you may need to use a conditional proof sequence as part of a larger proof, and you may need to use one conditional proof sequence tional sequence. The given numbered lines are the argument's premises, and the line begining with a single slsh is the argument's conclusion. Derive the argument's condusion in a series of new lines, using the proof checker below, In some cases path you can take to reach the conclusion. Click Begin Subproof to begin a new indented sequence, and click Add Line to add subsequent lines within the same sequence. To discharge an indented sequence and enter a non-indented fine, click End Subproof. You can check each tine 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 clusion in a series of new lines, using the proof checker below. In some cases, there may be more than one correc Hints for using conditional proof -> Begin Subproof Add Line 0

Explanation / Answer

G->(B->~N)   {premise}
~Gv(~Bv~N)   {switcheroo}
(~Gv~B)v~N   {Associative}
(~Bv~G)v~N   {commutative}
~Bv(~Gv~N)   {Associative}
B->(~Gv~N)   {switcheroo}   ...(i)

~Z->(Bv~G)   {premise}
Zv(Bv~G)   {switcheroo}
Zv(~GvB)   {commutative}
(Zv~G)vB   {Associative}
~(Zv~G)->B   {switcheroo}     ...(ii)

apply Hypothetical syllogism on (i) and (ii)

~(Zv~G)->(~Gv~N)
(~Z^~G)->(~Gv~N)   {Demorgan's law}
(~Z)->(~Gv~N)   {simplification}
~Z->(~Gv~N)   {simplification}
~Z->(G->~N)   {switcheroo}

Proved

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