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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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