Suppose a and b are schnittsDetermine whether Dst is a schni

Suppose a and b are schnitts.Determine whether D={s-t is a schnitt. If is isn\'tcheck to see which part of the definition of schnitt D does satisfy

Solution

Schnitts is the greatest numbers on the left side and smallest numbers on the right side

Let a be a set of less numbers on the right side then s belongs to a is also a schnitt.

Let b be a set of less numbers on the right side then t belongs to b is also a schnitt.

According to D = { s t | s a t b } is also schnitt .

Let \'a\' and \'b\' be the greater elements on the left side then D = { s t | s a t b } satisfys that and it is schnitt.

Let neither a and b are left or right sides then D = { s t | s a t b } is not a schnitt.