Prove that the relation ' friendship' is not an equivalence relation on the set of all people in chennai explain
Answers
Equivalence relation is a mathematical term that relates multiple elements or their combinations in a set of relations. For a relation to qualify as an equivalence relation, it must be transitive, reflexive and symmetric.
A symmetric relation means that if A is a friend of B, then B is also a friend of A. We know that this statement always holds good.
A reflexive relation means that if A is a friend of himself, then he should be a friend of A. For the given example, the statement does not have any meaning since a person being his own friend is an undefined statement.
A transitive relation means that if A is a friend of B and if B is a friend of C, then A should be a friend of C. However, we know from experience that this is not always true.
Hence, the relation ‘friendship’ is not an equivalence relation among all the people living in Chennai.