An equivalence relation is a relationship on a set that shows equality. An example of an equivalence relation on the set of integers is: 5 = 7 + x.
In the table below, R represents the relationship.
Property | General Example | Example With Real Numbers | Description |
---|---|---|---|
Reflexive | a R a | 5 = 5 | A relationship is reflexive if, for every member a of the set, a R a. |
Symmetric | a R b implies b R a | If a = b then b = a | A relationship is symmetric if, for every relation a R b on the set, b R a holds. |
Transitive | a R b and b R c implies a R c | If a = b and b = c, then a = c | A relationship is transitive if, the relationships a R b and b R c imply a R c. |
Table 1 |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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