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  1. 6)
  2. 1 2 3 4
  3. 1 1 1 1 1
  4. 2 0 1 1 1
  5. 3 0 0 1 1
  6. 4 0 0 0 1
  7.  
  8. Reflexive: Yes, the diagonal elements (1,1), (2,2), (3,3), and (4,4) are 1’s
  9. Symmetric: No. In order for the set to be symmetric all (a,b) in set much have a matching (b,a).
  10. Antisymmetric: Yes, there isn’t a 1 on both sides of the diagonal reflexive line. This means the matrix is antisymmetric.
  11. Transitive: Yes, it is transitive. The given set includes the transitive closure which is also an empty set.
  12. Partial Order: Yes, the given set is reflexive, antisymmetric, and transitive. These are the guidelines for partial order.
  13. Total Order: Yes, by definition of the trichotomy law.
  14. Well Order: Yes, a well ordered set using binary will always contain the lowest value.
  15. Equivalence Relation: This is not an equivalence relation because the set is not symmetric.
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