How from the directed graph I Know that if it\'s symmetric or not , and to know

Question

How from the directed graph I Know that if it's symmetric or not , and to know if it is anti-symmetric or not ? Properties of Relations Examples 4.3 Consider the following directed graph of a relation R on the set A= {a, b, c, d, e). From this diagram we can see that: (i) R is not reflexive, since there is no avow from c to itself, for example. (ii) R is symmetric, but not anti-symmetric, since every arrow connecting distinct points is bidirectional. (iii) R is not transitive since there are arrows from a to d, and from d to b, but not from a to b.

Explanation / Answer

A relationship is symmetric if, for every two elements you select, when a R b holds then b R a MUST be a member of the relatoin as well. When a relationship is symmetric, it doesn't automatically mean it is not anti-symmetric. Anti-symmetry means nothing more than the following: IF a R b AND b R a THEN a = b.

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