In the first part of this paper, we gave several different definition of convex functions and equivalent proposition.

本文首先归纳总结了凸函数的几个不同的定义，并说明其等价性。

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In this article we apply formal matrices technique to get a equivalent proposition of Li Shanian identity, and hence give an elementary proof for Li Shanlan identity.

本文应用形式矩阵的计算技巧，得到李善兰恒等式的一个等价命题，进而给出李善兰恒等式的一个初等证明。

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This research paper of proposition logic algebra in the said, on the basis of the solution of equations by polynomial, propositional formula for equivalent conversion and deductive reasoning.

在对命题逻辑代数化表示的基础上，通过解多项式方程组，对命题公式进行等价转换、演绎推理。

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"The object of California's establishment of the legal relationship of domestic partnership is to grant committed same-sex couples rights equivalent to those accorded a married couple. but Proposition 8, by depriving same-sex couples of the right to marry, denies them the dignity, respect, and stature accorded similarly situated opposite-sex couples under state law, " the court brief said.

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The discount is by far the better proposition, but the supposedly clever students viewed them as equivalent.

ECONOMIST: How marketers can take advantage of consumers�� innumeracy