Indifference curves cannot intersect
Transitivity of choice would be violated if indifference curves intersect.
If IC1 and IC2 intersected at C in Figure 4.5, this implies combination A is indifferent to C as they both lie on IC2, and that combination B is also indifferent to C as they lie on IC1. Under the assumption of transitivity, A should therefore be indifferent to B. However, this cannot be true since B contains more of both goods and must therefore yield greater utility. Transitivity must therefore have been violated.
The implication of the above is that only one indifference curve can pass through each point between the x and y axes.