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That is, the "middle" position, that Socrates is neither mortal nor not-mortal, is excluded by logic, and therefore either the first possibility (Socrates is mortal) or its negation (it is not the case that Socrates is mortal) must be true. An example of an argument that depends on the law of excluded middle follows. [10] We seek to prove that
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
The third and fourth are declarative sentences but, lacking meaning, are neither true nor false and therefore are not (or do not make) statements. The fifth and sixth examples are meaningful declarative sentences, but are not statements but rather matters of opinion or taste. Whether or not the sentence "Pegasus exists."
In formal languages, truth functions are represented by unambiguous symbols.This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives.
Indirect yes–no questions can be expressed using if or whether as the interrogative word: Ask them whether/if they saw him. Negative questions are formed similarly; however, if the verb undergoing inversion has a contraction with not , then it is possible to invert the subject with this contraction as a whole.
Two of them also use emphasis to make the meaning clearer. The last example is a popular example of a double negative that resolves to a positive. This is because the verb 'to doubt' has no intensifier which effectively resolves a sentence to a positive. Had we added an adverb thus: I never had no doubt this sentence is false.
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The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the ground that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act that is argued to be self-defeating. [27]