In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is {AND,NOT}, consisting of binary conjunction and negation. The singleton sets {NAND} and {NOR} are also functionally complete.
![f : X \to \mathbb{B}](/Images/godic/202501/14/b04301a1720366e329591064663deec04443.png")
，这里的 ![X\!](/Images/godic/202501/14/e043d9e4dac9f977a9dda15a0a000ac04443.png")
是一个任意集合而 ![\mathbb{B}](/Images/godic/202501/14/a8bd866de68eefd62bf12459c0a082e24443.png")
是一个通用的 2-元素集合，典型为 ![\mathbb{B} = \{ 0, 1 \} = \{ \mathrm{false}, \mathrm{true} \}](/Images/godic/202501/14/36836890edbbd6444d4d00c02a9e49fd4443.png")
，特别是生成所有的有限布尔函数，![f : \mathbb{B}^k \to \mathbb{B}](/Images/godic/202501/14/2918a1e9401bf31f05a4588a989cc32f4443.png")
。