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| 1. |
State and prove fundamental theorem on equivalence relation |
| Answer» LET '~' denote an EQUIVALENCE relation over some nonempty set A, called the universe or underlying set. Let G denote the set of bijective functions over A that PRESERVE the partition structure of A: ∀x ∈ A ∀g ∈ G (g(x) ∈ [x]). ... (This is the Fundamental Theorem of Equivalence Relations, MENTIONED above); | |