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Truth table

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A table expressing the truth values of a compound proposition in terms of the truth values of the simple propositions making it up (cf. Truth value). A truth table has the form of the table below, in which T denotes "true" and F denotes "false" . In it, are propositional variables, is a propositional formula, and the truth value of is determined by the truth values of . Each row in the table corresponds to one of the possible combinations of truth values of the propositions. Also, is the truth value of if the have the truth values indicated in the -th row.'
<tbody> </tbody>
T T
T F
F F

In mathematical logic, truth functions, corresponding to such logical connectives as negation, conjunction, disjunction, implication, and equivalence, are defined using truth tables. In classical propositional calculus, truth tables are used in the verification of the general validity of formulas: A formula is generally valid if and only if in the last column of its table all are T's.


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References

[a1] S.C. Kleene, "Introduction to metamathematics" , North-Holland (1951) pp. 288
[a2] W.S. Hatcher, "Foundations of mathematics" , Saunders (1968)
How to Cite This Entry:
Truth table. V.E. Plisko (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Truth_table&oldid=14099
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098