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

From Anti-symmetric Relation on Set to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Thousandths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 03:45 PM

    Thousandths Place in Decimals
    When we write a decimal number with three places, we are representing the thousandths place. Each part in the given figure represents one-thousandth of the whole. It is written as 1/1000. In the decim…

    Read More

  2. Hundredths Place in Decimals | Decimal Place Value | Decimal Number

    Jul 20, 24 02:30 PM

    Hundredths Place in Decimals
    When we write a decimal number with two places, we are representing the hundredths place. Let us take plane sheet which represents one whole. Now, we divide the sheet into 100 equal parts. Each part r…

    Read More

  3. Tenths Place in Decimals | Decimal Place Value | Decimal Numbers

    Jul 20, 24 12:03 PM

    Tenth Place in Decimals
    The first place after the decimal point is tenths place which represents how many tenths are there in a number. Let us take a plane sheet which represents one whole. Now, divide the sheet into ten equ…

    Read More

  4. Representing Decimals on Number Line | Concept on Formation of Decimal

    Jul 20, 24 10:38 AM

    Representing decimals on number line shows the intervals between two integers which will help us to increase the basic concept on formation of decimal numbers.

    Read More

  5. Decimal Place Value Chart |Tenths Place |Hundredths Place |Thousandths

    Jul 20, 24 01:11 AM

    Decimal place value chart
    Decimal place value chart are discussed here: The first place after the decimal is got by dividing the number by 10; it is called the tenths place.

    Read More