Open Branches Sometimes trees have more than one open branch.

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Presentation transcript:

Open Branches Sometimes trees have more than one open branch. It is important you know how to handle this situation.

Open Branches PvQ -(P&Q) PvQ | P&Q

Open Branches PvQ -(P&Q) PvQ | P&Q

Open Branches The (-&) Rule: -(A&B) -A -B PvQ -(P&Q) PvQ | P&Q

Open Branches The (-&) Rule: -(A&B) -A -B PvQ -(P&Q) -P -Q PvQ | P&Q 1

Open Branches PvQ -(P&Q) -P -Q PvQ | P&Q 1

Open Branches The (v) Rule: AvB A B PvQ -(P&Q) -P -Q PvQ | P&Q 1

Open Branches The (v) Rule: AvB A B PvQ -(P&Q) -P -Q PvQ | P&Q 1 P Q

Open Branches The (v) Rule: AvB A B PvQ -(P&Q) -P -Q PvQ | P&Q 1 P Q * * WRONG!

Open Branches The (v) Rule: AvB A B PvQ -(P&Q) -P -Q PvQ | P&Q 1 P Q * * WRONG! THE RESULT OF APPLYING A RULE MUST APPEAR ON EVERY OPEN BRANCH BELOW THE PLACE IT IS APPLIED.

Open Branches RIGHT The (v) Rule: AvB A B PvQ -(P&Q) -P -Q PvQ | P&Q 1 THE RESULT OF APPLYING A RULE MUST APPEAR ON EVERY OPEN BRANCH BELOW THE PLACE IT IS APPLIED.

Open Branches PvQ -(P&Q) -P -Q PvQ | P&Q 1 P Q * P Q * P is T Q is F

Open Branches PvQ -(P&Q) -P -Q PvQ | P&Q 1 INVALID P Q * P Q * P is T Q is F

Open Branches PvQ -(P&Q) -P -Q PvQ | P&Q 1 INVALID P Q * P Q * P is F Q is T The argument has two counterexamples.

For more click here Open Branches PvQ -(P&Q) -P -Q PvQ | P&Q 1 INVALID If there are two or more open branches don’t combine them to construct a counterexample. P Q * P Q * P is F Q is T The argument has two counterexamples. For more click here