
An argument is valid if and only if:

If the premises are true, then the conclusion must be true.

The premises are true and the conclusion is true.

If the conclusion is true, then the premises must be true.

The premises are true if and only if the conclusion is true.

An argument is shown to be valid on the table method if and only if:

There is no counterexample.

There is at least one counterexample.

There is no row on which all formulas are false.

There is a row on which all the premises are true and the conclusion is true.

On the table method, a counterexample is:

A row on which the premises are false and the conclusion is true.

A row on which the premises are true and the conclusion is false.

A and B are both counterexamples.

Neither A nor B are counterexamples.

If one of the premises in an argument is a contradiction, then:

The argument must be valid, because any conclusion can follow from a contradiction.

The argument must be invalid, because no valid argument contains a contradiction.

It might be valid, it might be invalid, we would need to know more about the argument.

If one of the premises in an argument is a tautology, then:

The argument must be valid, because any conclusion can follow from a tautology.

The argument must be invalid, because no valid argument can contain a tautology.

It might be valid, it might be invalid, we would need to know more about the argument.

If the conclusion of an argument is a tautology, then:

The argument must be valid because tautologies are always true.

The argument must be invalid because tautologies cannot be false.

It might be valid, it might be invalid, we would need to know more about the argument.

If the conclusion of an argument is a contradiction, then:

The argument must be valid because anything follows from a contradiction.

The argument must be invalid because contradictions are always false.

It might be valid, it might be invalid, we would need to know more about the argument.


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Not enough information.