In 22-29, find all greatest, least, maximal, and minimal elements for the relation in each of the referenced exercises.

Exercises 17(b)

To find:

All greatest, least, maximal and minimal elements for the “subset” relation on the set

S={0,1,2}.

Given information:

S=(0,1,2)

Concept used:

Maximal, Minimal, Least element.

Calculation:

To find the greatest element, least element maximal and minimal element of S=(0,1,2), first find the power set of S i.e.

P(S)={Φ,{0},{1},{2},{0,1},{0,2},{1,2},{0,1,2}}

Now, draw the Hasse diagram of “subset” relation on P(S).

Now from the Hasse diagram, it is clear that

Greatest element is {0,1,2}, because for all b in P(S), b is related to {0,1,2}