Anti-symmetric Relation on Set (advance math)

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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.


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.


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