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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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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

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Toolbox:
  • 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$
$R:\{(x,y):x+y =10\qquad x,y \in 10\}$
 
$R=\{(1,4),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2)(9,1)\}$
 
$(1,1),(2,2) \neq R$
 
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
 

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