Name: $\mathbb B_2=\langle\{0,1\},\vee,0,\wedge,1,'\rangle$

Elements: 0,1

0=0

1=1

Complement = negation = $1-x$ =

Alternative notation: $-x=\overline x=x^-=\neg x$

Join = or = truncated addition = $\min\{x+y,1\}$ =

Meet = and = multiplication =

Symmetric difference: $x\oplus y=(x\vee y)\wedge(x\wedge y)'$ = $(x\wedge y')\vee(y\wedge x')$

Implication: $x\to y=x'\vee y$

Bi-implication: $x\leftrightarrow y=(x\to y)\wedge(y\to x)$

Nand: $x|y=(x\wedge y)'$

Nor: $x\downarrow y=(x\vee y)'$

This algebra generates the variety of all Boolean algebras.

Every Boolean algebra is a subdirect product of $\mathbb B_2$.

none

4-element Boolean algebra $\mathbb B_2^2$

1-element Boolean algebra $\mathbb B_1$

4-element Boolean algebra $\mathbb B_2^2$

One-element algebras

???