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Jan. 31, 2023•0 likes•3 views

Jan. 31, 2023•0 likes•3 views

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difference between; reflexive, transitive, symetric and antisymetric relations Solution 1. Reflexive Relation: R is a relation in A and for every a ÃŽ A, (a,a) ÃŽ R then R is said to be a reflexive relation. Example: Every real number is equal to itself. Therefor \"is equal to \" is a reflexive relation in the set of real numbers. 2. Symmetric Relation: R is a relation in A and (a,b) ÃŽ R implies (b,c) ÃŽ R then R is said to be a symmetric relation. Example: In the set of all real numbers \"is equal to\" relation is symmetric. 3. Anti-Symmetric Relation: R is a relation in A. If (a,b) ÃŽ R and (b,a) ÃŽ R implies a = b, then R is said to be an anti-symmetric relation. Example: In set of all natural numbers the relation R defined by \"x divides y if and only if (x,y) ÃŽ R\" is anti-symmetric. For x|y and y|x then x = y. 4. Transitive Relation: R is a relation in A if (a,b) ÃŽ R and (b,c) ÃŽ R implies (a,c) ÃŽ R is called a transitive relation. Example: In the set of all real numbers the relation \"is equal to\" is a transitive relation. For a = b, b = c implies a = c. .

- 1. difference between; reflexive, transitive, symetric and antisymetric relations Solution 1. Reflexive Relation: R is a relation in A and for every a ÃŽ A, (a,a) ÃŽ R then R is said to be a reflexive relation. Example: Every real number is equal to itself. Therefor "is equal to " is a reflexive relation in the set of real numbers. 2. Symmetric Relation: R is a relation in A and (a,b) ÃŽ R implies (b,c) ÃŽ R then R is said to be a symmetric relation. Example: In the set of all real numbers "is equal to" relation is symmetric. 3. Anti-Symmetric Relation: R is a relation in A. If (a,b) ÃŽ R and (b,a) ÃŽ R implies a = b, then R is said to be an anti-symmetric relation. Example: In set of all natural numbers the relation R defined by "x divides y if and only if (x,y) ÃŽ R" is anti-symmetric. For x|y and y|x then x = y. 4. Transitive Relation: R is a relation in A if (a,b) ÃŽ R and (b,c) ÃŽ R implies (a,c) ÃŽ R is called a transitive relation. Example: In the set of all real numbers the relation "is equal to" is a transitive relation. For a = b, b = c implies a = c.