SOLUTION: Use natural deduction to derive the conclusion in each problem.
Use conditional proof or indirect proof as needed:
1.
F ⊃ (J ∨ ∼F)
2.
J ⊃ (L ∨ ∼J)
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Proofs
-> SOLUTION: Use natural deduction to derive the conclusion in each problem.
Use conditional proof or indirect proof as needed:
1.
F ⊃ (J ∨ ∼F)
2.
J ⊃ (L ∨ ∼J)
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Instead of a horsehoe symbol, I'm going to use an arrow symbol -> to indicate an conditional statement.
Let's do a conditional proof. This is because the statement we want to derive, F -> L, is a conditional statement. Its in "if...then" form. If we assume the antecedent F, and can somehow derive L, then we have proven that F leads to L and therefore F -> L is the case.
So we start with statement F (line 3 in the table below)
Then we use line 1 and line 3 to free up J v ~F to get what you see on line 4. Use the modus ponens rule.
Next use disjunctive syllogism with lines 4 and 3 so that you free up a J symbol. This forms line 5.
This then helps us use modus ponens again to get L v ~J (use lines 2 and 5), which is line 6
Using disjunctive syllogism a final time has us go from L v ~J to just L (use lines 6 and 5) which is line 7.
Line 3 starts with F. Through a bunch of logical statements, we are able to get to L on line 7. So we have shown that assuming F is the case leads to L being the case as well. Therefore F -> L has been proven.
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Here is how your derivation table should look like if you used a conditional proof approach
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