Greenwood press
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book-20600
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- SYMBOLIC LOGIC
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135 Ultracapacitors Unfolding the human brain ▲ ▼ ▲ SYMBOLIC LOGIC The nineteenth-century mathematician George Boole is the acknowledged founder of modern symbolic logic. He recognized that an algebra of logic could be developed following the model of the algebra of real numbers. The variables of the algebra are statements that have one of two values: TRUE (1) or FALSE (0). The fundamental operations are NOT, AND, and OR, as opposed to the num- ber operations of opposite, multiplication, and addition. The algebra of logic underlies decision-making, modern electronics, library searches, and branching in computer programs. Computer software is built on logical structures. If a market analyst had to select all of the California residents who were female from a computer database of customers in the United States, the status of each person in the database would be evaluated with an expression such as “this person is from California and this person is a women.” Sarah Jones (female) from San Francisco would evaluate as TRUE for both parts. Amy Redfox (female) from Arizona would be evaluated as FALSE AND TRUE. Since Amy misses one criterion, she should be excluded from the final set. Hence the value for Amy should be FALSE AND TRUE = FALSE. Although there may be millions of people in the database, each one falls into only one of four categories of logic. If you use a spreadsheet program, you can build truth tables that show the relationships among NOT, AND, and OR for these four cases. In the table below, all possible cases of statements p and q are listed using the words TRUE and FALSE. Each case has been evaluated with the spreadsheet’s functions for logic. For example, the spreadsheet formula in cell D2 is = AND(A2,B2). The formula in cell E4 is = OR(A4,B4). The last column gives truth values of an expression that uses of all of the Boolean operations. Download 1.81 Mb. Do'stlaringiz bilan baham: |
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