Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
0 votes

Each of the following defines a relation on $ N : (ii)\quad x+y=10,x,y\quad N$

Determine which of the above relation is

A) reflexive

B) symmetric

C) transitive.

Note: This is the 2nd part of a  4 part question, which is split as 4 separate questions here.

Can you answer this question?

1 Answer

0 votes
  • 1. A function R defined on A reflexive if $(x,x) \in R\;for\;x \in A$
  • 2.A relation R defined on A is symmetric if $(x,y) \in R =>(y,x) \in R \qquad x,y \in A$
  • 3. A relation R defined on A is transitive if $ (x,y) \in R (y,z) \in R =>(x_1,x_2) \in R. x,y,z \in A$
$R:\{(x,y):x+y =10\qquad x,y \in 10\}$
$(1,1),(2,2) \neq R$
Therefore R is not reflexive
$(1,9) \in R => (9,1) \in R$
This is true for all the element of R
Hence R is symmetric
Consider $(2,8) \in R (8,2) \in R$
but $(2,2) \in R$
R is not transitive
R is symmetric but neither reflexine nor transitive



answered Mar 4, 2013 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App