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Logic: Truth Tables

Logic: Truth Tables. Constructing a Truth Table. Truth Table. A truth table for a compound statement is a list of the truth or falsity of the statement for every possible combination of truth and falsity of its components.

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Logic: Truth Tables

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  1. Logic: Truth Tables Constructing a Truth Table

  2. Truth Table • A truth table for a compound statement is a list of the truth or falsity of the statement for every possible combination of truth and falsity of its components. • In other words, a truth table helps to show whether a statement is true or false.

  3. Rows • To find the number of rows used in a truth table, take the number 2 raised to the power of the number of variables. • For example, if there was a p statement and a q statement, there would be 2 variables, 2^2 is 4. • If there were three statements, it would be 2^3, or 8 rows.

  4. Columns • The columns under the connectives /\, and \/, stand for the conjunction, and disjunction of the expression on the two sides of that connective.

  5. Two statement table

  6. The three statement table

  7. Negation Truth Table

  8. Conjunction Truth Table

  9. Disjunction Truth Table

  10. Lets fill out a table

  11. Negate the p column

  12. Copy the q column

  13. Fill the /\ column

  14. Copy the p column

  15. Fill in the \/ column using the p and the /\ columns

  16. Use the final column to determine what type of statements it is

  17. Contingency • Some were true, while one was false. • That makes this statement a contingency.

  18. Real life example • In case that was not entirely clear, let’s take a look at an everyday example. • Circuits. There are two different kinds of circuits, a series circuit and a parallel circuit. • When the switch is closed the light will be on. However, with a series circuit, both switches have to be closed and with a parallel circuit only one switch has to be closed for the light to go on.

  19. Series Circuits

  20. Parallel Circuits

  21. Conclusion • That concludes the Logic: Truth Tables lesson. • For more information, consult Finite Mathematics by Berresford and Rockett. • Or learn logic online: http://www.earlham.edu/~peters/courses/log/terms2.htm

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