Logical conjunction ($\wedge$)

The conjunction $A\wedge B$ holds when both $A$ and $B$ hold.

An AND gate computes $a\wedge b=ab$ for bits $a,b$. It is irreversible when only its one-bit output is retained. The Toffoli gate embeds the operation reversibly as $(a,b,c)\mapsto (a,b,c\oplus ab)$; setting $c=0$ preserves the inputs while recording their logical conjunction.