Martinakom

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Category > Geometry Posted 14 Dec 2017 My Price 7.00

I have two questions that are giving me a really hard time. I've found mixed things about this topic online.

I have two questions that are giving me a really hard time. I've found mixed things about this topic online. I have a vague Idea about what to do but it seems like people get different answers for this one. The antisymmetry is particularly hard for me to prove. Please answer and explain why you found this particular answer. Thanks,

 

 

  1. Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}. Consider the relation ≤ defined on S as follows: ((x1, y1) ≤ (x2, y2) if x1 ≤ x2 and y1 ≤ y2. Draw the directed graph of this relation. Show that it is a partial order. Explain why it is not a total order. 
  2. Consider the set S defined in the previous problem problem and the following relation = defined on S as follows: (x1, y1) = (x2, y2) if x1 + y1 = x2 + y2. Draw the directed graph of this relation. Show that it is an equivalence relation. List its equivalence classes. 

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Martinakom
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Status NEW Posted 14 Dec 2017 02:12 PM My Price 7.00

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