About Me

My photo
"After retiring as Deputy Director, working on a project for nurturing Human Excellence through education by offering consultancy services to the Educational Institutions & Students as per their requirements. Organizing and contributing my share as Resource Person for In-service- programmes for professional growth of School Staff. Financial professionalism with optimum utilization of available resources.Extending the Counseling services to the Students through on-line service. Was awarded National Award for introducing innovative techniques of teaching Mathematics in Schools. Author of number of Text Books of Mathematics such as series of "Systematic Mathematics" for Primary Classes, (prescribed by the Royal Government of Bhutan for its primary classes), ABD's Composite Mathematics" for middle classes, etc. Delivered talks on All India Radio and participated in various group discussions on topics of current affairs etc.

How I can be of any help to my friends who are in need of educational consultancy?

Intraction with Teachers of Indore

Intraction with Teachers of Indore
Y.P.Verma's Interaction with teachers

Blog Archive

Monday, April 14, 2008

Some Doubt

In Mathematics Textbook for Class XII of N.C.E.R.T 2006 edition, question no. 8 Exercise 1.1 reads as:

Show that the relation R in the set A = {1,2,3,4,5} given by
R = {(a,b) : Ia-bIis even} is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}.

My doubt is:

Can we say that "the relation R in the set A = {1,2,3,4,5} given by
R = {(a,b) : Ia-bIis even} is an equivalence relation"?

In fact this will be true if relation R is reflexive. That is if a R a for all a belonging to A.

Which means that 1 - 1 = 0 is even.

Can we say ' 0 is even'?

Please comment.

No comments: