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.