Conjunction, AND Gate

Definition¹

The following Boolean function is called the $\text{AND}$ gate or logical conjunction and is denoted as follows.

$$ \land : \left\{ 0, 1 \right\}^{2} \to \left\{ 0, 1 \right\} $$

$$ 0\land 0 = 0,\quad 0\land 1 = 0,\quad 1\land 0 = 0,\quad 1\land 1 = 1 $$

Explanation

The $\text{AND}$ gate sends two truth values to one truth value, and returns true only when both truth values are true.

부울 함수	기호	진리표
$\text{AND}$		$a$ $b$ $a \land b$ $0$ $0$ $0$ $0$ $1$ $0$ $1$ $0$ $0$ $1$ $1$ $1$

This can be expressed with $\text{NOT}$ gate and $\text{OR}$ gate.

$$ a \land b = \lnot(\lnot a \lor \lnot b) $$