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a meaningful declarative sentence that is true or false, [citation needed] or; a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence. [1] [2] In the latter case, a (declarative) sentence is just one way of expressing an underlying statement.
For instance, two statements or more are logically incompatible if, and only if their conjunction is logically false. One statement logically implies another when it is logically incompatible with the negation of the other. A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one ...
A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false. The sentences "Is the water boiling?"
See if you can determine what’s fact and what’s fiction in our listing of 105 true or false statements. From facts about food and geography, to statements on holidays and even Disney, we'll ...
A statement is "vacuously true" if it resembles a material conditional statement , where the antecedent is known to be false. [1] [3] [2]Vacuously true statements that can be reduced (with suitable transformations) to this basic form (material conditional) include the following universally quantified statements:
A proposition (true or false) asserting an atomic fact is called an atomic proposition. — Russell, "Introduction to Tractatus Logico-Philosophicus" See also [2] and [3] especially regarding elementary proposition and atomic proposition as discussed by Russell and Wittgenstein; Note the distinction between an elementary/atomic proposition and ...
Instead, comparison operators generate BIT(1) values; '0'B represents false and '1'B represents true. The operands of, e.g., &, |, ¬, are converted to bit strings and the operations are performed on each bit. The element-expression of an IF statement is true if any bit is 1.
A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).