Symmetric Relation

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A Symmetric Relation is a relation that is invariant to permutations of its relation arguments.



  • (Wikipedia, 2009) ⇒
    • In the case of symmetric functions, the value of the output is invariant under permutations of variables. From the form of an equation one may observe that certain permutations of the unknowns result in an equivalent equation. In that case the set of solutions is invariant under any permutation of the unknowns in the group generated by the aforementioned permutations. For example
    • Definition(symmetric relation): A relation [math]\displaystyle{ R }[/math] on a set A is called symmetric if and only if for any a, and b in A, whenever &lta, b> R, &ltb, a> [math]\displaystyle{ R }[/math].
    • Example 5: The relation = on the set of integers {1, 2, 3} is {<1, 1>, <2, 2> <3, 3> } and it is symmetric. Similarly = on any set of numbers is symmetric. However, < (or >), (or on any set of numbers is not symmetric.
    • Example 6: The relation "being acquainted with" on a set of people is symmetric.