The document discusses antisymmetric and symmetric relations. It provides the example of the less than or equal to relation (<=) on real numbers as an antisymmetric relation, since if a <= b and b <= a, then a must equal b. The example given in the question of comparing real numbers to exponentials is shown not to be antisymmetric. A symmetric relation is defined such that if a relates to b, then b also relates to a, with examples given as equivalence relations where a relates to b if and only if they are equal, or a relation where the absolute value of the difference between a and b is a constant.