Symmetric Relation
A relation is symmetric if for any two elements: if (a,b) is in the relation, then (b,a) is also in it.
In other words: if the connection holds in one direction, it must also hold in the other direction.
Examples of Symmetric Relations
- The "x is sibling of y" relation is symmetric: if Anna is sibling of Béla, then Béla is also sibling of Anna.
- The "x is friend of y" relation (ideally) is symmetric: if Anna is friend of Béla, then Béla is also friend of Anna.
Counterexamples (Non-Symmetric Relations)
- The "<" relation is not symmetric: if 2 < 5, it is not true that 5 < 2.
- The "father-child" relation is also not symmetric: if Anna is father of Béla, it is still not true that Béla is father of Anna.
Summary
A relation is symmetric if it is always bidirectional. If we find a case where only one direction holds but not the other, then the relation is not symmetric.
Practice Exercise
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