Let us write symbolically
A.N = (A)
Which means that the operation of dichotomizing N according to A given the class frequency equal to (A). Similarly, we write
α.N = (α)
adding, we get
A.N + α.N = (A) + (α)
(A + α).N = (A) + (α)
(A + α).N = N
A + α = 1
Thus in symbolic expression we can replace A by (1 - α) and α by (1 – A).
Similarly, B can be replaced by (1 – β) and β by (1-B) and so on.
Dichotomizing (B) according to A, let us write
A.(B) = (AB)
Similarly, B.(A) = (BA)
A.(B) = B.(A) = (AB) = AB.N
Which accounts to dichotomizing N according to AB.
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