Suppose the conclusion of an argument is known to be tautologous. Do you have to do a truth table to know whether it is valid or invalid?

How do you determine if an argument is valid or invalid?

A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

How do you know if a truth table is invalid or valid?

In general, to determine validity, go through every row of the truth-table to find a row where ALL the premises are true AND the conclusion is false. Can you find such a row? If not, the argument is valid. If there is one or more rows, then the argument is not valid.

What is a Tautologous conclusion?

A valid argument with true premises has a true conclusion. So, the conclusion of a valid argument with premises that are tautologies is also true under every assignment. This implies that the conclusion is a tautology.

Why every argument with a Tautologous conclusion is valid?

An argument whose conclusion is a tautology MUST be valid! Since a tautology is always true an argument whose conclusion is a tautology never has a false conclusion. But if the conclusion of the argument is NEVER false, then there cannot possibly be an invalidating row, so the argument must be valid.

Can an invalid argument have true premises and true conclusion?

If an argument has all true premises and a true conclusion, then it is valid. FALSE: It is possible for an argument to have all true premises and a true conclusion but still be invalid.

Can a valid argument have false premises and a true conclusion?

A valid argument can have false premises; and it can have a false conclusion. But if a valid argument has all true premises, then it must have a true conclusion.

When an argument is valid and its premises are true the argument is called?

More specifically, we ask whether the argument is either deductively valid or inductively strong. A deductive argument is an argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument’s premises are true.