Anti-symmetric Relation on Set

What is anti-symmetric relation onset?

Let A be a set in which the relation R defined.

R is said to be anti-symmetric, if there exist elements, if

aRb and bRa  ⇒ a = b

that is, (a, b) ∈ R and ((b, a) ∈ R ⇒ a = b.

A relation R in A is not anti-symmetric, if there exist elements a, b ∈ A, a ≠ b such that aRb and bRa.


For example, the relation defined by ‘x is less than or equal to’ in the set of real numbers is be anti-symmetric, as a ≤ b and b ≤ a imply a = b, where a, b are elements of the set.

● Set Theory

● Sets

● Representation of a Set

● Types of Sets

● Pairs of Sets

● Subset

● Practice Test on Sets and Subsets

● Complement of a Set

● Problems on Operation on Sets

● Operations on Sets

● Practice Test on Operations on Sets

● Word Problems on Sets

● Venn Diagrams

● Venn Diagrams in Different Situations

● Relationship in Sets using Venn Diagram

● Examples on Venn Diagram

● Practice Test on Venn Diagrams

● Cardinal Properties of Sets






7th Grade Math Problems

8th Grade Math Practice

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