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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 β a = b
that is, (a, b) β R and ((b, a) β R β a = b.
A relation R in A is not anti-symmetric, if there exist elements a, b β A, a β b such that aRb and bRa.
For example, the relation defined by βx is less than or equal toβ in the set of real numbers is be anti-symmetric, as a β€ b and b β€ a imply a = b, where a, b are elements of the set.
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