Below is a basic Truth Table where p can represent the first argument and q for the second argument.

+-----+-----+-------+-------+
|  p  |  q  | p ∧ q | p ∨ q |
+-----+-----+-------+-------+
|  T  |  T  |   T   |   T   |
|  T  |  F  |   F   |   T   |
|  F  |  T  |   F   |   T   |
|  F  |  F  |   F   |   F   |
+-----+-----+-------+-------+

Suppose that we use the operators AND ∧ and OR ∨ to verify arguments like so:

p - Samson is longhaired

q - Petrucci is longhaired

p∧q - Samson and Petrucci are longhaired

This works well for the above example.

However, are there cases where the truth table is not reliable as a basis for proving the validity of arguments?