We say that two real number a and y are related xRy if x ySo

We say that two real, number a and y are related, xRy, if |x -y|

(a) This is not an equivalence relation.

(b) For reflexive : - x belongs to R then xRx is implies that |x- x| < 1

= |0|<1

which is true,therefore |x - y| < 1 is reflexive.

For symmetry :- let x, y belongs to R. if xRy then yRx

xRy which is implies that |x - y|<1

= | y- x| <1

= yRx therefore | x - y|<1 is symmetry

For transitive : let x , y and z belongs to R

if |x - y| <1 and |y- z|<1 then | x - z|<1

for |x - z| = | x - y + y - z| ( add and subtract y )

= |(x - y) + (y - z)| ( by triangle inequality )

< | x - y| + | y -z | ( from given condition)

< 1 + 1

< 2 so which is not equal to |x - z|<1 therefore this is not transitive