.. _logic:

論理
=====

.. Logic
.. =====

.. In the last chapter, we dealt with equations, inequalities,
.. and basic mathematical statements like
.. ":math:`x` divides :math:`y`."
.. Complex mathematical statements are built up from
.. simple ones like these
.. using logical terms like "and," "or," "not," and
.. "if ... then," "every," and "some."
.. In this chapter, we show you how to work with statements
.. that are built up in this way.

前章では，等式や不等式，そして「 :math:`x` は :math:`y` を割り切る」のような基本的な数学的命題を扱いました．複雑な数学的命題はこのような単純な文から，「かつ」，「または」，「もし～ならば」，「すべての」，「ある～が存在する」といった論理の用語を用いて構築されます．この章では，このように構築された文をどのように扱うかを紹介します．

.. include:: C03_Logic/S01_Implication_and_the_Universal_Quantifier.inc
.. include:: C03_Logic/S02_The_Existential_Quantifier.inc
.. include:: C03_Logic/S03_Negation.inc
.. include:: C03_Logic/S04_Conjunction_and_Iff.inc
.. include:: C03_Logic/S05_Disjunction.inc
.. include:: C03_Logic/S06_Sequences_and_Convergence.inc