translations with explanations

translations with explanations - More on Translations N....

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More on Translations N. Apostol Key: D: It's a dog C: It's a cat. M: It's a mammal. I. NEITHER this NOR that / NOT this AND NOT that ('this', 'that' means anything what-so-ever, no matter whether simple or complex, no matter what the topic) (a) It's neither a cat nor a dog. same as: (b) It's NOT a cat AND NOT a dog. Major operator/connective is a conjunction (between two negated atomic statements) (c) It's NOT a cat OR a dog. ~ ( C v D ). Major connective is a negation ( of a disjunction between two atomic statements). All three statements above are logically equivalent: they propose/reveal the same content (information), they propose the same meaning, they communicate the same information. In other words, the same information/meaning/content can be read off apparently different logical forms when the atomic statements (C, D in this case) are given meaning/content (when they spell out something in English). Contructing the truth table for each of the above statements results in the two statements agreeing in truth-values in each line (identical columns under their respective major connective). Moreover, creating a bi-conditional between the two statements, the bi-conditional is a tautology. RULE of Bi-Conditional/Rule of replacement/Rule of logical equivalence : Two statements are logically equivalent IF AND ONLY IF their biconditional is tautologous. So, whenever this happens between two statements, each statement can be replaced by the other without loss of
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translations with explanations - More on Translations N....

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