R is a relation on a set N of natural numbers defined by

R={(x,y): y = nx , n element of N} check whether R is reflexive, symmetric and transitive.

Asked by fleurnym | 3rd May, 2020, 04:50: PM

Expert Answer:

Given relation is R={(x,y): y = nx , n element of N}
F o r space n equals 1 comma space x equals n x
T h e r e f o r e comma space open parentheses x comma space x close parentheses element of R
T h e r e f o r e comma space R space i s space r e f l e x i v e
L e t space left parenthesis x comma space y right parenthesis element of R space space rightwards double arrow space y equals n x
rightwards double arrow space x equals n y space space w h e n space space n equals 1
T h e r e f o r e comma space R space i s space s y m m e t r i c space f o r space n equals 1.
L e t space left parenthesis x comma space y right parenthesis comma left parenthesis y comma space z right parenthesis element of R space space rightwards double arrow y equals n x space space a n d space space z equals n y
z equals n y equals n left parenthesis n x right parenthesis equals n squared y comma space n squared element of N
T h e r e f o r e comma space R space i s space t r a n s i t i v e.

Answered by Renu Varma | 3rd May, 2020, 10:58: PM