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Truth Tables - Online Term Paper

Truth Tables

An Introduction to Formal (Symbolic) Logic

Unit One: Truth Tables

We have seen a few problems encountered when trying to study logic in natural language (i.e., in English). For example, we examined semantic fallacies; and in our informal logic unit we saw the difficulties in judging the strengths of arguments when we encountered ambiguous language.

Logicians have tried to address these problems by inventing an artificial language to better determine the truth-value of sentences, the validity of arguments, and other logical concerns.

Some logicians see symbolic logic's use in a similar manner to the advantage Arabic numerals give us over Roman numerals. After all, which is ...

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simply be shown as a letter (e.g., ``L'' for ``Lansing''); this would be called an atomic sentence.

b. A compound sentence (e.g., ``Either Detroit is the capital of Michigan , or Lansing is the capital of Michigan .'') needs more than just two letters (because it would just say ```D' `L''' or `` Detroit is the capital of Michigan ; Lansing is the capital of Michigan .'') and that is something different from the original sentence containing the word ``or'').

So, symbolic logic uses binary functions (since they link two concepts) to combine simple, atomic sentences into compound, molecular sentences. There are four examples of these connectives.

i. The conjunction is a molecular sentence with the word ``and'' (and sometimes ``but'') in it. The symbol for the conjunction is either the ``&'' or the ``''. Each part of the conjunction is known as either the left conjunct or right conjunct.

ii. The disjunction is a molecular sentence with the word ``or'' in ...

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would do the problem in the following order: 3+2; 5-1; 4+2.

Truth-Table Answer Key(s)

2. After translation, sentences (now in symbolic form) can be ``worked'' to solve for their truth-values; the method we will first use is called truth tables. A truth table graphically shows all the possible truth-values a sentence can have; the different atomic sentences are shown on the left side of the table and the sentence that is to be ``solved'' is shown on the right (see ``hints for setting up a truth table''). Take the quiz on Michigan cities to fill in the truth tables for the negation, conjunction, and the disjunction.

a. Answer the question with a ``T'' for ``true,'' or an ...

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PAPER DETAILS

Added: 2/28/2012 03:43:01 PM
Submitted By: stache59
Category: Miscellaneous
Type: Premium Paper
Words: 2039
Pages: 8

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