Conjunction

The conjunction or AND of a set of operands is true only when all of them are true. With two inputs, $X\wedge Y$ is $1$ only when $X=1$ and $Y=1$.

$X$	$Y$	$X\wedge Y$
0	0	0
0	1	0
1	0	0
1	1	1

Conjunction is the analogue of set intersection: an element is in $A\cap B$ if and only if it’s in both. The corresponding hardware element is the AND gate.

In digital circuits, a series connection of two switches realizes AND — current flows from one end to the other only if both switches are closed. In CMOS this is subtler: stacking two NMOS transistors in series in the pull-down network does compute ”$A$ AND $B$” as a conduction condition (the path conducts only when both gates are high), but conducting in the pull-down pulls the gate output low — so the output is $\overline{A\cdot B}$, i.e. NAND, not AND. To get an AND output, you put a NAND followed by an inverter. See CMOS for the full PUN/PDN duality.

Notation

The symbol in formal logic and Boolean algebra is $\wedge$. In electronics, AND is usually written without a symbol (juxtaposition: $XY$) or with a dot ($X\cdot Y$). In code, you’ll see & (bitwise AND) or && (short-circuit AND, evaluates the second operand only when the first is true).

A common identity to remember: $X\wedge 1=X$ (identity), $X\wedge 0=0$ (annihilation), and $X\wedge \overline{X}=0$ (complementation). See Boolean Algebra for the full set of laws.