1. In logic, a truth function is a function that takes one or more truth values and returns a truth value as output.
在逻辑中，真值函数是一个接受一个或多个真值并返回一个真值作为输出的函数。

2. The truth function AND returns true only if both of its inputs are true.
与真值函数仅在其输入都为真时返回真。

3. Truth functions can be represented using truth tables, which show all possible combinations of inputs and their corresponding outputs.
真值函数可以用真值表表示，显示所有可能的输入组合及其相应的输出。

4. The truth function XOR returns true if exactly one of its inputs is true.
异或真值函数在其输入中有且仅有一个为真时返回真。

5. Truth functions play a fundamental role in the study of propositional logic and predicate logic.
真值函数在命题逻辑和谓词逻辑的研究中起着基础性作用。

6. Understanding how truth functions operate is essential for analyzing the validity of logical arguments.
理解真值函数的运作方式对于分析逻辑论证的有效性至关重要。