1. A more complex example: (L&E)>P | L>P
Calculating Validity
A more complex example: (L&E)>P | L>P

2. Calculating Validity A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L E P
(L&E)>P | L>P

3. Calculating Validity A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L T
F T F F
T F E
T T F F P
T T T TF F F F
(L&E)>P | L>P

4. Calculating Validity A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L T
F T F F
T F E
T T F F P
T T T TF F F F
(L&E)>P | L>P

5. Calculating Validity A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L T
F T F F
T F E
T T F F P
T T T TF F F F
(L&E)>P | L>P

6. Calculating Validity A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L T
F T F F
T F E
T T F F P
T T T TF F F F
(L&E)>P | L>P

7. Calculating Validity A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L T
F T F F
T F E
T T F F
(L&E)>P | L>P P
T T T TF F F F T
T T T F
T T T
T T T F
F T

8. Calculating Validity Counterexample
A more complex example: (L&E)>P | L>P
Here we have 3 variables, so we need
to list all the ways L, E and P can be T or F. L T
F T F F
T F E
T T F F P
T T T TF F F F
(L&E)>P | L>P T
T T T F
T T T
T T T F
F T
Counterexample
The argument is INVALID.

9. What happens if there are fourL T
F T F F
T F E
T T F F P
T T T TF F F F R
Four Variables
What happens if there are four
or more variables
in the argument?

10. What happens if there are fourL T
F T F F
T F E
T T F F P
T T T TF F F F R
Four Variables
What happens if there are four
or more variables
in the argument? T
F T F F
T F

11. What happens if there are fourL T
F T F F
T F E
T T F F P
T T T TF F F F R
Four Variables
What happens if there are four
or more variables
in the argument? T
F T F F
T F
T T F F

12. What happens if there are fourL T
F T F F
T F E
T T F F P
T T T TF F F F R
Four Variables
What happens if there are four
or more variables
in the argument? T
F T F F
T F
T T F F
T T T TF F F F

13. What happens if there are fourL T
F T F F
T F E
T T F F P
T T T TF F F F R
T T T T T T T T F F F F F F F F
Four Variables
What happens if there are four
or more variables
in the argument? T
F T F F
T F
T T F F
T T T TF F F F

14. What happens if there are fiveL T
F T F F
T F E
T T F F P
T T T TF F F F R
T T T T T T T T F F F F F F F F : S
T T T T T T T T T T T T T T T T :
Five Variables
What happens if there are five
or more variables
in the argument? T
F T F F
T F :
T T F F
T T F F :
T T T TF F F F :
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