More Complex Formulas
As shown above, the CASE (IF c THEN b ELSE a ) connective is constructed either from the 2-argument connectives IF...THEN... and AND or from OR and AND and the 1-argument NOT. Connectives such as the n-argument AND (a & b & c & ... & n), OR (a V b V c V ... V n) are constructed from strings of two-argument AND and OR and written in abbreviated form without the parentheses. These, and other connectives as well, can then used as building blocks for yet further connectives. Rhetoricians, philosophers, and mathematicians use truth tables and the various theorems to analyze and simplify their formulas.
Electrical engineering uses drawn symbols and connect them with lines that stand for the mathematicals act of substitution and replacement. They then verify their drawings with truth tables and simplify the expressions as shown below by use of Karnaugh maps or the theorems. In this way engineers have created a host of "combinatorial logic" (i.e. connectives without feedback) such as "decoders", "encoders", "mutifunction gates", "majority logic", "binary adders", "arithmetic logic units", etc.
Read more about this topic: Propositional Formula
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