$a r b$ indicates that a relation $r$ is symmetric if whenever $a$ is related to $b$ through $r$, then $b$ is also related to $a$. This property is crucial in understanding equivalence relations, as symmetry helps establish a balanced connection between elements in a set. If a relation is symmetric, it implies that the relationship between elements does not depend on the order in which they are considered, reinforcing the idea of mutual connection among related elements.
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