Consdier the relation defined by took a class with defined o

Consdier the relation defined by \"took a class with\" defined on the set of students. Explain why this relation is not an equivalence relation.

Solution

Say R= took a class with

1) R is reflexive as x Rx as every student took classs with him/her self

2) if xRy ie x took class with y then y took class with x

yRx

R is symetric

3)xRy and yRz

x took class with y and y took class with z

Then it is not necessary that x took class with z { if x took class with y yesterday and y toom class with z a day before yestarday then x did not took class with z .

Hence R is not equivalance.