contrapositive

简明释义

英[ˌkɒntrəˈpɒzɪtɪv]美[ˈkɑːntrəˈpɑːzəˌtɪv]

adj. 对换的；对照的

n. 对换句

英英释义

单词用法

同义词

反义词

例句

1.The contrapositive is equally true.

这个反命题同样是正确的。

2.This hostile became so habitual that Nike pompously formed a contrapositive section for this rank only.

这种敌对变得很习惯，耐克傲慢地组成了这支队伍的对换节只。

3.While according to the statistical data, the experimental group has more higher trend than contrapositive group in efficient respects of all medical standards.

但根据数据的统计观察，在各项疗效判定标准的总的有效率方面，试验组有高于对照组的趋势。

4.As we know, contrapositive symmetry is the tautology in classical logic.

众所周知，在古典逻辑中，逆否对称性是永真公式。

5.While according to the statistical data, the experimental group has more higher trend than contrapositive group in efficient respects of all medical standards.

但根据数据的统计观察，在各项疗效判定标准的总的有效率方面，试验组有高于对照组的趋势。

6.The contrapositive is true, too.

对换一下也是正确的。

7.If a shape is a square, then it has four equal sides; its contrapositive is that if a shape does not have four equal sides, then it is not a square.

如果一个形状是正方形，那么它有四条相等的边；它的反命题是，如果一个形状没有四条相等的边，那么它就不是正方形。

8.The contrapositive of a conditional statement is always logically equivalent to the original statement.

条件语句的反命题总是与原始语句在逻辑上等价。

9.In logic, understanding the contrapositive can help clarify arguments and proofs.

在逻辑中，理解反命题可以帮助澄清论点和证明。

10.When proving a theorem, one can often use the contrapositive to establish the result more easily.

在证明定理时，人们通常可以使用反命题更容易地建立结果。

11.The statement 'If it rains, then the ground is wet' has a contrapositive: 'If the ground is not wet, then it does not rain.'

陈述“如果下雨，那么地面是湿的”有一个反命题： “如果地面不湿，那么就没有下雨。”

作文

In the realm of logic and mathematics, understanding the concept of a contrapositive is crucial for forming valid arguments and proofs. The contrapositive of a statement is derived from its original form by negating both the hypothesis and the conclusion and then switching their places. For instance, if we take the conditional statement, "If P, then Q," the contrapositive would be "If not Q, then not P." This transformation is not merely a linguistic exercise; it has profound implications in logical reasoning.To illustrate the significance of the contrapositive, consider the statement: "If it rains, then the ground is wet." The contrapositive would be: "If the ground is not wet, then it has not rained." Understanding this relationship allows us to infer that the truth of the original statement guarantees the truth of its contrapositive. In formal logic, this principle is essential because it ensures that if we can prove the contrapositive, we have effectively proven the original statement as well.This property of the contrapositive is particularly useful in mathematical proofs, especially in areas such as number theory and geometry. For example, when proving that a number is even, one might state: "If a number is even, then it is divisible by 2." The corresponding contrapositive would be: "If a number is not divisible by 2, then it is not even." Proving the contrapositive can sometimes be more straightforward than proving the original statement directly.Moreover, the contrapositive plays a significant role in everyday reasoning and critical thinking. When evaluating arguments, recognizing the contrapositive can help identify logical fallacies or strengthen conclusions. For instance, in a debate about climate change, one might argue: "If human activity contributes to global warming, then we must take action." The contrapositive here would be: "If we do not take action, then human activity does not contribute to global warming." By analyzing the contrapositive, one can see the implications of inaction and reinforce the necessity of addressing climate issues.In conclusion, the concept of the contrapositive is a powerful tool in both formal logic and practical reasoning. It allows us to derive equivalent statements that can simplify complex arguments and enhance our understanding of relationships between conditions. By mastering the contrapositive, we improve our ability to think critically and argue effectively, whether in academic settings or everyday discussions. Thus, the contrapositive serves not only as a fundamental concept in mathematics but also as a valuable asset in our intellectual toolkit, helping us navigate the complexities of logic and reasoning in various aspects of life.

在逻辑和数学的领域中，理解对立命题的概念对于形成有效的论证和证明至关重要。对立命题是通过否定一个陈述的假设和结论并交换它们的位置来推导出的。例如，如果我们取条件陈述“如果P，那么Q”，那么对立命题就是“如果不是Q，那么不是P”。这种变换不仅仅是语言上的练习；它在逻辑推理中具有深远的意义。为了说明对立命题的重要性，考虑这个陈述：“如果下雨，那么地面是湿的。”对立命题将是：“如果地面不湿，那么没有下雨。”理解这种关系使我们能够推断原始陈述的真实性保证了其对立命题的真实性。在形式逻辑中，这一原则至关重要，因为它确保如果我们能证明对立命题，我们就有效地证明了原始陈述。对立命题的这个特性在数学证明中尤其有用，特别是在数论和几何等领域。例如，在证明一个数字是偶数时，人们可能会说：“如果一个数字是偶数，那么它可以被2整除。”相应的对立命题将是：“如果一个数字不能被2整除，那么它不是偶数。”证明对立命题有时比直接证明原始陈述更简单。此外，对立命题在日常推理和批判性思维中也发挥着重要作用。在评估论点时，识别对立命题可以帮助识别逻辑谬误或加强结论。例如，在关于气候变化的辩论中，人们可能会争辩：“如果人类活动导致全球变暖，那么我们必须采取行动。”这里的对立命题将是：“如果我们不采取行动，那么人类活动不会导致全球变暖。”通过分析对立命题，人们可以看到不采取行动的影响，并强化解决气候问题的必要性。总之，对立命题的概念是一个强大的工具，无论是在形式逻辑还是实际推理中。它使我们能够推导出等效的陈述，从而简化复杂的论证并增强我们对条件之间关系的理解。通过掌握对立命题，我们提高了批判性思维和有效论证的能力，无论是在学术环境还是日常讨论中。因此，对立命题不仅作为数学中的基本概念，还作为我们智力工具箱中的宝贵资产，帮助我们驾驭生活各个方面中逻辑和推理的复杂性。