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
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● Subset
● Practice Test on Sets and Subsets
● Problems on Operation on Sets
● Practice Test on Operations on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
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