Partial order and total order
Not what you're looking for?
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?
Purchase this Solution
Solution Summary
This shows how to determine if something is a partial or total order.
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 ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.