Mathematics Homework Solutions
#5867
Proving a partial order and total order.
In each of the following say whether or not R is a partial order on A. If so, is it a total order?
a) A= {a,b,c,d}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)}
b) A is the set of positive divisors of 24, that is A= {1,2,3,4,6,8,12,24}, and the relation R is dividing. If B is the set of positive divisors of 24 except 1, what is the minimal element(s)? smallest element? maximal element(s)? largest element of B?
This shows how to determine if something is a partial or total order.
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