Proof of the Law of Association (optional material, p. 4)

For both cases we have now defined values for Xa and Yb such that the following three conditions all hold true:

Xa/xa

Ya/ya		    >    Xa

Yb		    >    Xb/xb

Yb/yb

(1)
0 < Xa < Xb

(2)
0 < Yb < Ya

(3)

From (1) we can also deduce two additional inequalities:

Xa(xa/Xa) - Yb(ya/Ya) < 0

(4)
Yb(yb/Yb) - Xa(xb/Xb) < 0

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