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