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While the above compound sentence is itself a statement, because it is true, the two parts, "Ganymede is a moon of Jupiter" and "Ganymede is a moon of Saturn", are themselves statements, because the first is true and the second is false. However, it is sometimes used to name something abstract that two different statements with the same meaning are both said to "express".
In this usage, the English sentence, "It is raining", and the French sentence "Il pleut", would be considered to express the same proposition; similarly, the two English sentences, "Callisto orbits Jupiter" and "Jupiter is orbitted by Callisto" would also be considered to express the same proposition.
287 BCE), did recognize a need for the development of a doctrine of "complex" or "hypothetical" propositions, i.e., those involving conjunctions (statements joined by "and"), disjunctions (statements joined by "or") and conditionals (statements joined by "if...
then..."), but their investigations into this branch of logic seem to have been very minor.
then...", "because", and "necessarily", are all operators.
A logical operator is said to be on the truth or falsity of the statements from which they are constructed.
These are, of course, cornerstones of classical propositional logic.
There is some evidence that Aristotle, or at least his successor at the Lyceum, Theophrastus (d.
Hence, the truth or falsity of a statement using the operator "necessarily" does not depend entirely on the truth or falsity of the statement modified.A is any word or phrase used either to modify one statement to make a different statement, or join multiple statements together to form a more complicated statement.In English, words such as "and", "or", "not", "if ..., is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements.
In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement.Joining two simpler propositions with the word "and" is one common way of combining statements.