Chapter 5 - The Non-Subderivation Rules of SD

Question 1

Conjunction Introduction

Answer 1

Specifies that if P and Q occur on earlier lines of a derivation that we may enter P & Q on a subsequent line. Here the rule template should not be taken as specifying the order in which P and Q must be derived before P & Q can be entered.

| P
|
| Q
|
| ▶️ P & Q

Question 2

Conjunction Elimination

Answer 2

Specifies that if a conjunction on an earlier line of a derivation then we may enter on a subsequent line either the left conjunct or the right conjunct of the conjugation.

Or

| P & Q
|
|
▶️ Q

P & Q
|
|
▶️ P

Question 3

Disjunction Introduction

Answer 3

Specifies that if a sentence P occurs on an earlier line of a derivation then we may enter on a subsequent line either P v Q or Q v P, where Q is any sentence of SL.

Question 4

Conditional Elimination

Answer 4

Specifies that if P Q and P occur on earlier lines of a derivation, in either order, then we may enter Q on a subsequent line.

Question 5

Biconditional Elimination

Answer 5

Specifies that if a sentence of the form P = Q and one of its immediate components (P or Q) occur on earlier lines of a derivation, in either order, then we may enter on a subsequent line the other immediate component.