Question

Explain Antisymmetric relation with an example

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Answer 1

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For example, 12 is divisible by 4, but 4 is not divisible by 12. The usual order relation ≤ on the real numbers is antisymmetric: if for two real numbers x and y both inequalities x ≤ y and y ≤ x hold then x and y must be equal.

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Answer 2

Answer:

In mathematics, a homogeneous relation R on set X is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other. More formally, R is antisymmetric precisely if for all a and b in X

if R(a, b) with a ≠ b, then R(b, a) must not hold,

or, equivalently,

if R(a, b) and R(b, a), then a = b.

(The definition of antisymmetry says nothing about whether R(a, a) actually holds or not for any a.)

Explanation:

For example, 12 is divisible by 4, but 4 is not divisible by 12. The usual order relation ≤ on the real numbers is antisymmetric: if for two real numbers x and y both inequalities x ≤ y and y ≤ x hold then x and y must be equal.

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