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An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.
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An equivalence relationship is a relationship over the set of integers defined for as follows:For equivalence modulo n (n being a positive integer),a ~ b (mod n) n divides (a-b)This partitions the set of integers into n equivalence classes: {0, 1, 2, ... , n-1}.
An Equivalence fallacy is the error of defining distinct and conflicting items in similar terms, thus equating tow items that are not, in fact, equal. An author who suggests that one act of serious wrongdoing does not differ from a minor offence commits the fallacy of moral equivalence. A different kind of Equivalence Fallacy is used when, for example, a politician argues: "Yes, I used illegal money to fund my campaign ... but so did my opponent!" This type of moral equivalence fallacy is called the "tu quo" argument ("But you're one too!").
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