As explained in this article, the values false and true should not be confused with the integers 0 and 1, but may be identified with the elements of the Galois field (finite field) of two elements (see here).
A field is a set with two operations that satisfy certain axioms.
The symbols 0 and 1 are conventionally used to denote the additive and multiplicative identities of a field because the real numbers are also a field (but not a finite one) whose identities are the numbers 0 and 1.
The additive identity is the element 0 of the field, such that for all x:
x + 0 = 0 + x = x
and the multiplicative identity is the element 1 of the field, such that for all x:
x * 1 = 1 * x = x
The finite field of two elements has only these two elements, namely the additive identity 0 (or false), and the multiplicative identity 1 (or true).
The two operations of this field are the logical XOR (+) and the logical AND (*).