Use the algorithm given in the text to find a topological sorting for the relation of exercise 20.

To find:

A topological sorting for the “ R ” relation on the set s={0,1},

where R is defined by (a,b,c)R(d,e,f)⇔a≤d, b≤e and c≤f.

Given information:

S={0,1}

Concept used:

(a,b,c) and (d,e,f) in S×S×S,

(a,b,c)R(d,e,f)⇔a≤d, b≤e and c≤f

Calculation:

The minimal element is (0,0,0) so start with (0,0,0).

The beginning of the total order is:

Total order: (0,0,0)

Set A1=A−{(0,0,0)}. You can indicate this by removing (0,0,0) from the Hasse diagram as

Shown below.

Next, choose the minimal element from A1−{(0,0,0)}. You have three choices

(0,1,0), (1,0,0) and (0,0,1) .Say you pick (0,0,1). The total order thus far is

Total order: (0,0,0) &(0,0,1)

Set A1=A−{(0,0,0)}−{(0,0,1)}=A−{(0,0,0)(0,0,1)}