Relational closures are widely used in mathematics and daily life. For example, in mathematics, the less than () relation is not reflexive, but its reflexive closure is less than or equal to (≤) or greater than or equal to (≥), but it is reflexive. In mathematics, less than relation is often used to express the relationship between quantities, but sometimes it is inconvenient to use less than relation, but less than or equal to relation is actually the relationship between quantities. We unconsciously use reflexive closures less than. In daily life, we are grouped according to age, class or citizen relationship. Generally speaking, the relationship of the same age, class and citizen refers to the relationship between two different people, which is not reflexive. If we agree that we are the same age, the same class and the same townsman, then they will be reflexive at this time. If only one person is different from others, then a group can be formed.

The less than relation is asymmetric, and its reciprocal is greater than the relation. However, when the two relationships are combined (the relationship is regarded as a set), the unequal relationship is symmetrical, the unequal relationship is a symmetrical closure less than or greater than the relationship, the relationship between husband and wife is asymmetrical, and the relationship between wife and husband is asymmetrical, but the symmetrical closure marriage relationship is symmetrical (considering the equality between men and women, that is, symmetrical). The relationship greater than 1 is not. Relationships greater than 2 are also transitive ... All transitive closures of relationships greater than 1, greater than 2, greater than 3, ... are combined to obtain transitive closures of relationships greater than 1, but transitive closures of parent-child relationships are transitive.