If an argument is invalid, then there is an interpretation where all the premises are true and the conclusion is false. So If the conclusion is a tautology, the argument must be valid since the conclusion can’t be false under any interpretation.
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Can an invalid argument have a tautology as a conclusion?
Therefore, if the premises of a propositionally valid argument are tautologies, then its conclusion must be a tautology as well.
No propositionally valid argument can have a contradiction as a conclusion.
| P | (P∧¬P) | ¬(P→P) |
|---|---|---|
| T | F | F |
| F | F | F |
Is a tautology a valid argument?
A tautology is not an argument, but rather a logical proposition. A logical argument may contain tautologies. To be a valid logical argument (using the traditional rules of predicate logic), not only do all of your statements need to be true, but the argument needs to prove the statement being argued.
What is a tautological argument?
A tautological argument is otherwise known as a circular argument, that is, one that begins by assuming the very thing that is meant to be proven by the argument itself.
What is an invalid argument with a true conclusion?
The conclusion is actually true but this fact does NOT follow from the claim that the premises are true. We can imagine a fantasy in which the premises are true but the conclusion is still false.
Can a tautology be invalid?
If an argument is invalid, then there is an interpretation where all the premises are true and the conclusion is false. So If the conclusion is a tautology, the argument must be valid since the conclusion can’t be false under any interpretation. Thank you for your answer.
Can tautologies be invalid?
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.
Which is a tautology?
A tautology is a logical statement in which the conclusion is equivalent to the premise. More colloquially, it is formula in propositional calculus which is always true (Simpson 1992, p.
What is a valid tautology?
A Tautology is a statement that is always true because of its structure—it requires no assumptions or evidence to determine its truth. A tautology gives us no genuine information because it only repeats what we already know.
What is the meaning of tautological?
Definition of tautological
1 : involving or containing rhetorical tautology : redundant. 2 : true by virtue of its logical form alone.
What is an invalid argument?
Similarly, arguments may be described as valid or invalid, but statements cannot. An argument is said to be an invalid argument if its conclusion can be false when its hypothesis is true. An example of an invalid argument is the following: “If it is raining, then the streets are wet.
Is every argument with a tautological conclusion sound?
No. A valid argument may have a true conclusion even if not all its premises are true. For instance: (Premise) All cats are flying creatures.
Is a tautology always true?
A tautology is a compound statement in Maths which always results in Truth value. It doesn’t matter what the individual part consists of, the result in tautology is always true.
How do you identify tautology?
If you are given any statement or argument, you can determine if it is a tautology by constructing a truth table for the statement and looking at the final column in the truth table. If all of the truth values in the final column are true, then the statement is a tautology.
Which statement is the tautology statement?
Note: The students must know that Tautology is a statement which is always true. Here, we can clearly see that since in option C we have $p \vee \sim p$ which is no matter what is always going to be true always. Hence, we have the option C as a tautology.
| p | q | $ \sim q$ |
|---|---|---|
| F | F | T |
Why is tautology used?
Tautology is a literary device whereby writers say the same thing twice, sometimes using different words, to emphasize or drive home a point. It can be seen as redundancy, a style fault that adds needless words to your idea, statement, or content; or it can be defended as poetic license.
Which of the following is an example of tautologies?
In a logical tautology, the statement is always true because one half of the “or” construction must be so: Either it will rain tomorrow or it won’t rain. Bill will win the election or he will not win the election. She is brave or she is not brave.
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