Chapter 8 Natural Deduction Proofs

Question 1

What is Natural Deduction?

Answer 1

Natural deduction consists in using
inference rules to derive the conclusion of an argument from its premises.

Question 2

What is the reiteration inference rule?

Answer 2

Introduction again at a new line any statement that has already appeared previously in the derivation.

R:

Question 3

What is the Ampersand Elimination inference rule?

Answer 3

If we have a conjunction at a line in our derivation, we can introduce either conjunct of the conjunction at a new line in the derivation.

&E:

Question 4

What is the Ampersand Introduction inference rule?

Answer 4

If we have a statement of any kind at a line in our derivation and a statement of any kind at another line in our derivation, we can introduce the conjunction of those two statements at a new line in the derivation.

&I:

Question 5

What is the Vee introduction inference rule?

Answer 5

if we have a statement of any kind at a line in our derivation, we can introduce
the disjunction of that statement and any other of symbolic logic we might like at
a new line in the derivation.

vI:

Question 6

What is the Arrow Elimination inference rules?

Answer 6

If we have a conditional statement at a line in our derivation and we have the antecedent of that conditional at another line in our derivation, we can introduce the consequent of the conditional at a new line in the derivation.

->E:

Question 7

What is the Vee Elimination inference rules?

Answer 7

If we have a conjunction of conditional statements with the same consequent at a
line in our derivation and the disjunction of the antecedents of the two conditionals at another line in our derivation, we can introduce the consequent of the two conditionals at a new line in the derivation.

vE:

Question 8

What is the Double-Arrow Introduction inference rule?

Answer 8

If we have a conjunction of conditionals at a line in a derivation in which (i) the antecedent of the first is the consequent of the second and (ii) the consequent of the first is the antecedent of the second, we can introduce a biconditional at a
new line with the antecedent and consequent of the first conditional on either side of the double arrow

<->I:

Question 9

What is the Double-Arrow Elimination inference rule?

Answer 9

If we have biconditional at a line in a derivation, we can introduce a conjunction of conditionals at a new line in which (i) the first component of the biconditional is the antecedent of the first conditional and the consequent of the second and (ii)the second component of the biconditional is the consequent of the first conditional and the antecedent of the second.

<->E: