Question about specifics of boolean-algebra

Question

Why does it use only 1 and 0 in boolean algebra? But can you explain it without attracting logic gates. Thank you

Answer 1

See Two-element Boolean algebra (but it does not use only $0$ and $1$ symbols; there are variables: $x,y,\ldots$ and $=$ and $\land, \lor$, etc.)

The reason for the choice of $1$ and $0$ to represent $\text {True}$ and $\text {False}$ are historical.

See George Boole's The Mathematical Analysis of Logic (1847).

In the "class" interpretation of the calculus, Boole denotes with $1$ the "universe" from which variables $x$ and $y$ take their meaning.

The "minus" sign is the complement operation: $1-x$, and thus we have $0$, the complement of the "universe", i.e. the null class.

In the "propositional" interpretation of the calculus, the "hypothetical universe", $1$, shall comprehend all conceivable cases.

And see page 51:

The symbol $1 - x$ selects those cases in which the proposition $x$ is false. But if the proposition is true, there are no such cases in its hypothetical universe, therefore $1-x = 0$, or

$$x=1.$$

The elective symbol $x$ selects all those cases in which the proposition is true, and therefore if the proposition is false,

$$x = 0.$$