In the world of nature (Its a priori is "Fact"), if we apply mathe to measure the fact, 2+2=5 is false so it requires a re-examination.
By contrast, in the world of words (Logic, Social Science, History, and Law), the story is different from these previously mentioned worlds.
When there are two individuals, A and B, A*B is considered as the public/community composed of the individualities, A and B. Thus, in the world of words, there is always an incidentally created component which cannot be explained by either Mathe rule or natural science.
In econometrics, when we run the regression analysis based on these symbolic logic algebra, the formula should be
Y = β_0 + β_1 * A + β_2 * B + β_3 * (A*B)
Let's denote the dependent valuable "Y" is the sum of utility of A and B and the public/community A*B.
β_0 is an intercept which can be explained as neither A nor B.
β_1 is a coefficient of the individual A,
β_2 is a coefficient of the individual B,
and then β_3 is a coefficient of the public/community A*B.
A union of "A" and "B" produces "A", "B", and "A*B" (The intercept of A and B). When both "A" and "B" contain a quantity of 2 in itself, and "A*B" contains a quantity of 1, then (A=2)+(B=2)=A+B+A*B=2+2+1=
When "A∪B = "A+B-(A∩B)" is described as an arithmetric function "A+B+(A*B)", Let Y the answer for "A∪B" = "A+B-(A∩B)" = "A+B+(A*B)",
∀ Y ∈ ( X_1, X_2, X_3 ),
∃ i ∈ (1,2,3), and ∀ X_i ∈ (0, 1),
∀ A ∈ ( X_1, X_2, X_3 )
∀ B ∈ ( X_1, X_2, X_3 )
Then, A∈(0. 1) and also B∈(0, 1),
For example,
A_i ∈ ( 1, 1, 0 ) = 2
B_i ∈ ( 0, 1, 1) =2 ,
then
A*B ∈ ( 0, 1, 0 ) =1
When A=2, B=2,
Y = A + B = 2 + 2 = "A∪B = "A+B-(A∩B)" = "A+B+(A*B)"= 2 + 2 + 1 = 5
∴ 2 + 2 = 5
