All tables are judged from just one column, the one under the main operator. It summarizes all the other columns. They are not examined in judging the proposition or argument at the top of the table.
A single proposition is always either true or false. However, in some circumstances it may not be possible to determine which.
The truth value of a single proposition may be either a matter of its form or a matter of its relationship to reality.
A tautology or formal truth is true irrespective of the truth values of its component propositions. Its truth table is true in every row.
A self-contradiction or formal falsehood is false irrespective of the truth values of its component propositions. Its truth table is false in every row.
A contingency is neither tautological nor self-contradictory. Its truth table is true in some rows and false in others.
A pair of propositions may be either logically related or factually related.
A logically equivalent pair have the same truth value irrespective of the truth values of their component propositions. In each row, their truth tables have identical main operator values where they have the same input values. An equivalent pair are also consistent if there is a row in which they are both true. In Exercise 6.3 this option is not to be taken but it is in Exercise 6.5.
A contradictory pair have the opposite truth value irrespective of the truth values of their component propositions. In each row, their truth tables have different main operator values where they have the same input values.
A pair can also be neither logically equivalent nor contradictory. If there are rows in which they are both true, then they are consistent (though not equivalent). If there is no row in which they are both true, they are inconsistent (though not contradictory).
An argument can be either valid or invalid.
A valid argument cannot have an assignment which makes each premise true and its conclusion false. Thus in its truth table, no row has all the premise main operator values as true and the conclusion main operator value as false.
An argument which is not valid is invalid. Thus in its truth table, one or more rows have all the premise main operator values as true and the conclusion main operator value as false. Such a row proves that the argument is invalid.