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
bRa ⇒ a = b
(a, b) ∈ R
and ((b, a) ∈ R ⇒ a = b.
R in A is not anti-symmetric,
if there exist elements a, b ∈ A, a ≠ b such that aRb and bRa.
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
● Representation of a Set
● Types of Sets
● Pairs of Sets
● 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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