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

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

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

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

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

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

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

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

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

10. 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.

11. 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.

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

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

14. 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.

15. 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