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Let defined by such that .
a) Find the values of and . Since iff we concluse that Taking itno aaccount that and we conclude that and
b) Let and the relation < be defined on L such that x < y if x divides y. Draw the Hasse diagram.
The Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point is drawn for each element of the poset, and line segments are drawn between these points according to the following two rules:
1. If in the poset, then the point corresponding to appears lower in the drawing than the point corresponding to .
2. The line segment between the points corresponding to any two elements and of the poset is included in the drawing iff covers or covers .
In our case, if and only if Therefore, the Hasse diagram is the following:
c) The functions and are inverse of one another if and that is and for any and