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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?

Solution Preview

a. R is not a partial order. Since d belongs to A, so by the reflexive property of partial order, (d,d) should belong to R. But it doesn't. So R is not a partial order.
R is not a total order. Since a total order must be at first a partial ...

Solution Summary

This shows how to determine if something is a partial or total order.

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