R is a symmetric relation on a? B(a∈A∧b∈A∧aRb→bRa). When R on A is symmetric, it is said that R is symmetric on A, or the relationship R on A is symmetric.

For example, the relations I = {< x, y > | x, y are equal} and n = {< x, y > | x, y are unequal} in the set of numbers are all symmetrical relations; And l = {< x, y > | x less than y} is not symmetric. When the relation r on a is symmetric, its complementary relation and inverse relation are symmetric.

Extended data:

The reasoning of symmetry relation can be expressed by the following formula: R(a, b)→R(b, a). Or: aRb, so, bRa. Here R stands for symmetry, and A and B are two kinds of objects respectively. Symmetric relation inference rule: If R(a, b) is judged to be true, then R(b, a) is also true.

Relationship judgment is a simple judgment to judge the relationship between objects. Simple judgment includes not only nature judgment, but also relationship judgment, that is, the judgment of the relationship between objects.

Note that anti-symmetric relation is not the antonym of symmetric relation (aRb → bRa). Some relationships are both symmetric and antisymmetric, such as "equal". Some relationships are neither symmetric nor anti-symmetric.

Relationship judgment is different from nature judgment. Nature judgment is to judge whether an object has a certain nature (that is, the relationship between object and nature), and there is only one subject; Relationship judgment is to judge whether there is a relationship between objects, and this relationship always exists between two or more objects. So there are two or more objects in the relationship judgment, that is, at least two subjects.

Baidu Encyclopedia-Anti-symmetric Relationship

Baidu Encyclopedia-Symmetry Relationship