Can a statement be both tautology and contradiction?
A tautology is a formula which is “always true” — that is, it is true for every assignment of truth values to its simple components. You can think of a tautology as a rule of logic. The opposite of a tautology is a contradiction, a formula which is “always false”.
What if one of the premises is either a tautology or a contradiction?
Conclusion : an argument with contradictory premises is valid. So my conclusion is.. If “one or more of premises is contradiction” or “conclusion is tautology”, argument is always valid.
Can an argument be valid if the premises are contradictory?
Well, if the premises are contradictory, then they cannot all be true (that’s just what contradictory means) so they can’t all be true while the conclusion is false (the necessary condition for non-validity). So the argument cannot be non-valid, it must be valid. Thus an argument with contradictory premises is valid.
Can an argument with a contradictory conclusion be valid?
Yes, an argument with contradictory premises is deductively valid. That’s because it’s impossible to have all its premises true and its conclusion false (since its premises can never all be true)*.
Is the statement a tautology a self contradiction or neither?
A compound statement is a tautology if its truth value is always T, regardless of the truth values of its variables. It is a contradiction if its truth value is always F, regardless of the truth values of its variables.
What is tautology contingency and contradiction?
A compound proposition that is always true for all possible truth values of the propositions is called a tautology. • A compound proposition that is always false is called a contradiction. • A proposition that is neither a tautology nor contradiction is called a contingency.
Can a contradiction be an argument?
Contradictory premises involve an argument (generally considered a logical fallacy) that draws a conclusion from inconsistent or incompatible premises. Essentially, a proposition is contradictory when it asserts and denies the same thing.
Can an argument have all true premises and a true conclusion yet not be deductively valid?
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 all false premises?
A valid argument can have all false premises and a true conclusion.
What is the difference between tautologies and contradiction with example?
A proposition is a tautology if it is true under all conditions. A proposition is a contradiction if it is false under all conditions. The column of a tautology in a truth table contains only 1’s. The column of contradiction in a truth table contains only 0’s.
Is P ∧ Q → Pa contradiction?
A statement that is always false is known as a contradiction. Example: Show that the statement p ∧∼p is a contradiction.
Are all contradictions logically equivalent?
So, because tautologies always have the same truth value (namely, true), they are always logically equivalent. Moreover, two contradictions (sentences (or propositions) whose truth value is always “false”) are also logically equivalent.
Can a tautology be contingent?
If the proposition is true in every row of the table, it’s a tautology. If it is false in every row, it’s a contradiction. And if the proposition is neither a tautology nor a contradiction—that is, if there is at least one row where it’s true and at least one row where it’s false—then the proposition is a contingency.
What is a compound proposition that is neither a tautology nor a contradiction?
A compound proposition that is neither a tautology nor a contradiction is called a contingency. Definition (Logical equivalence) Compound propositions p and q are called logically equivalent if p ↔ q is a tautology. The notation p ≡ q denotes that p and q are logically equivalent.
What do you call two proposition with the same truth values?
Logically Equivalent: ≡ Two propositions that have the same truth table result. Tautology: A statement that is always true, and a truth table yields only true results.
When two statements are combined by logical connective and then the compound statement is called?
So, the correct answer is that when two statement are connected connected by logical connective then the compound statement is called conjunctive statement.
When can we say that two propositions are logically equivalent?
The propositions are equal or logically equivalent if they always have the same truth value. That is, p and q are logically equivalent if p is true whenever q is true, and vice versa, and if p is false whenever q is false, and vice versa. If p and q are logically equivalent, we write p = q.
What do you call a declarative statement which is either true or false but not both?
Definition A proposition is a declarative sentence to which we can assign a truth- value of either true or false, but not both.
Is a declarative sentence that is either true or false *?
A proposition is a declarative sentence that is either true (denoted either T or 1) or false (denoted either F or 0). Notation: Variables are used to represent propositions. The most common variables used are p, q, and r.
What is the statement using a declarative sentence and always true or false?
More specifically, geometry and logic uses a precise kind of declarative sentence that is either definitely true or false; such declarative sentences are called statements.