ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Binary cartesian set product ▼ Binary relation ▼ Map ▼ Function ▼ Real collection function ▼ Euclidean real function ▼ Real function ▼ Rational function ▼ Integer function ▼ Natural number function ▼ Boolean function
Definition D5402
Boolean logic gate

Let $\mathbb{B} = \{ 0, 1 \}$ be the D217: Set of boolean numbers.
A D18: Map $f : X \to Y$ is a boolean logic gate if and only if
 (1) $$\exists \, N \in 1, 2, 3, \ldots : X = \mathbb{B}^N$$ (2) $$Y = \mathbb{B}$$

A D18: Map $f : X \to Y$ is a boolean logic gate if and only if
 (1) $$\exists \, N \in 1, 2, 3, \ldots : X = \{ 0, 1 \}^N$$ (2) $$Y = \{ 0, 1 \}$$
Children
 ▶ D3554: AND boolean logic gate ▶ D3552: Conditional basic boolean logic gate ▶ D5394: Falsum basic boolean logic gate ▶ D3551: NAND boolean logic gate ▶ D3556: NOR boolean logic gate ▶ D3550: NOT boolean logic gate ▶ D3555: OR boolean logic gate ▶ D5395: Verum basic boolean logic gate ▶ D3553: XNOR boolean logic gate ▶ D3557: XOR boolean logic gate