Browse Questions

# 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.

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