This is from the Daniel Bonevac Deduction text, page 122 #12.

Given premise (p -> q) -> p show p using deduction.

I can do this using made up rules on steps 4+5, not given in the book. The other steps are proper steps given in the book.

1. (p -> q) -> p.     A
2. Show p
3. | ¬p.              AIP
4. | ¬p -> ¬(p -> q)  made up rule. take contrapositive of conditional 1
5. | ¬(p -> q).       ->E, 4, 3
6. | ¬(¬p ∨ q).       made up rule. convert conditional 5 to disjunction form.
7. | (¬p ∨ q).        ∨I, 3

We've only covered conjunction exploitation/introduction, negation exploitation/introduction, indirect proof, reiteration, conditional exploitation, conditional proof, biconditional exploitation/introduction.

How could the the above proof be completed using only the given rules?

This is from the Daniel Bonevac Deduction text, page 122 #12.

Given premise (p -> q) -> p show p using deduction.

I can do this using made up rules on steps 4+5, not given in the book. The other steps are proper steps given in the book.

1. (p -> q) -> p.     A
2. Show p
3. | ¬p.              AIP
4. | ¬p -> ¬(p -> q)  made up rule. take contrapositive of conditional 1
5. | ¬(p -> q).       ->E, 4, 3
6. | ¬(¬p ∨ q).       made up rule. convert conditional 5 to disjunction form.
7. | (¬p ∨ q).        ∨I, 3

We've only covered conjunction exploitation/introduction, negation exploitation/introduction, indirect proof, reiteration, conditional exploitation, conditional proof, biconditional exploitation/introduction.

The fundamental rules covered:

&E: Conjunction Exploitation
&I: Conjunction Introduction
¬¬: Negation introduction/exploitation
AIP: Indirect Proof (Show p, then assume ¬p, derive contradiction, conclude and cancel Show)
R: Reiteration
->E: Conditional Exploitation
ACP: Conditional Proof (Show p->q, assume p, derive q, conclude and cancel Show)
I: Biconditional introduction
E: Biconditional exploitation

How could the the above proof be completed using only the given rules?

This is from the Daniel Bonevac Deduction text, page 122 #12.

Given premise (p -> q) -> p show p using deduction.

I can do this using made up rules on steps 4+5, not given in the book. The other steps are proper steps given in the book.

1. (p -> q) -> p.     A
2. Show p
3. | ~p.              AIP
4. | ~p -> ~(p -> q)  made up rule. take contrapositive of conditional 1
5. | ~(p -> q).       ->E, 4, 3
6. | ~(~p ∨ q).       made up rule. convert conditional 5 to disjunction form.
7. | (~p ∨ q).        ∨I, 3

We've only covered disjunction exploitation/introduction, negation exploitation/introduction, indirect proof, reiteration, conditional exploitation, conditional proof, biconditional exploitation/introduction.

How could the the above proof be completed using only the given rules?

This is from the Daniel Bonevac Deduction text, page 122 #12.

Given premise (p -> q) -> p show p using deduction.

I can do this using made up rules on steps 4+5, not given in the book. The other steps are proper steps given in the book.

1. (p -> q) -> p.     A
2. Show p
3. | ¬p.              AIP
4. | ¬p -> ¬(p -> q)  made up rule. take contrapositive of conditional 1
5. | ¬(p -> q).       ->E, 4, 3
6. | ¬(¬p ∨ q).       made up rule. convert conditional 5 to disjunction form.
7. | (¬p ∨ q).        ∨I, 3

We've only covered conjunction exploitation/introduction, negation exploitation/introduction, indirect proof, reiteration, conditional exploitation, conditional proof, biconditional exploitation/introduction.

How could the the above proof be completed using only the given rules?