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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● **Problems on Operation on Sets**

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● **Venn Diagrams in Different Situations**

● **Relationship in Sets using Venn Diagram**

● **Practice Test on Venn Diagrams**

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