Phil 145 (001): Truth table examples
OR (inclusive)
A |
B |
A or B |
~A |
~B |
T |
T |
T |
F |
F |
T |
F |
T |
F |
T |
F |
T |
T |
T |
F |
F |
F |
F |
T |
T |
Argument
A or B
~B
Therefore, A
To demonstrate with the truth table, look at columns 3 and 5 (premises) and 1 (conclusion). Look at all cases when there are T in 3 and 5. If there's always a T in 1, then it is a valid arg (which it is).
This is not a valid arg:
A or B
A
Therefore, B
To demonstrate, look at columns 1 and 3 (premises) and 2 (conclusion). Notice in row 2 that you have T, F, T... so both premises can be true when the conclusion is false.
AND: try this yourself.
A |
B |
A and B |
~A |
~B |
T |
T |
? |
F |
F |
T |
F |
? |
F |
T |
F |
T |
? |
T |
F |
F |
F |
? |
T |
T |
Is this argument valid:
A and B
A
Therefore, B
Is this argument valid:
A
B
Therefore, A and B