Logic Rules Sheet Two
Rule 7. Addition (Abbreviated by "AD")

If "P" is an available line, any formula "Q" (available or not) can be added to P by putting a wedge "v" between them to make a new sentence "P v Q" or "Q v P" which may be written as a new line in the derivation. 	
Rule 8. Disjunctive Syllogism (Abbreviated by "DS")

If a disjunction and the negation of one of its disjuncts are both available lines, the other, non-negated disjunct may be written as a new line in the derivation. Thus:

If "P v Q" and "~Q" are both available lines, then "P" may be written as a new line.

If "P v Q" and "~P" are both available lines, then "Q" may be written as a new line.	
Rule 9. Commutativity (Abbreviated by "CM")

If any disjunction or conjunction is an available line, then that formula may be written with the postions of its conjuncts or disjuncts reversed. (The operator may not change.) Thus:

If "P ^ Q" is an available line, then "Q ^ P" may be written as a new line.

If "P v Q" is an available line, then "Q v P" may be written as a new line.	
Rule 10. Modus Ponens (Abbreviated by "MP")
If "P É Q" and "P" are both available lines, then "Q" may be written as a new line.	
Rule 11. Modus Tollens (Abbreviated by "MT")
If "P É Q" and "~Q" are both available, then "~P" may be written as a new line.	
Rule 12. Conditional Proof (Abbreviated by "CP")

IF, and ONLY IF, you first write a show line of "Show P É Q" you may write "P" as the next line, justifying it by "ACP," for "Assumption for Conditional Proof."

IF, and ONLY IF, you subsequently produce "Q" as an available line, and there is no other uncancelled "show" between that show line and that "Q", then that "show" may be cancelled, and a box may be drawn around that formula and any other lines there may be between it and it's show line. If the relevant show line is line #1, then the derivation is successfully finished. (Write "CP" by the show line.)	
Rule 13. Repetition (Abbreviated by "R") 
If "P" appears as an available line, then "P" may be written as a new line.