F o r space t h e space r e l a t i o n space R subscript 1 space d e f i n e d space o n space R space b y space t h e space r u l e space space space space left parenthesis a comma b right parenthesis element of space R subscript 1 space left right double arrow 1 plus space a b greater than 0 P r o v e space t h a t space colon space left parenthesis a comma b right parenthesis element of space R subscript 1 space a n d space left parenthesis b comma c right parenthesis space element of R subscript 1 rightwards double arrow left parenthesis a comma c right parenthesis space element of space R subscript 1 space i s space n o t space t r u e space f o r space a l l space a comma b comma c space element of space R.

Asked by ravikantmanchanda | 30th May, 2015, 06:11: PM

Expert Answer:

L e t space u s space t a k e space a comma b comma c space element of R F o r space left parenthesis a comma b right parenthesis left parenthesis a comma b right parenthesis space element of R subscript 1 I t space i m p l i e s space t h a t comma 1 plus a b greater than 0 F o r space a n y space t w o space n u m b e r s left parenthesis b comma c right parenthesis space element of R i t space i m p l i e s space t h a t comma 1 plus b c greater than 0  F o r comma 1 plus a b greater than 0 space a n d space 1 plus b c greater than 0 up diagonal strike rightwards double arrow 1 plus a c space greater than 0  F o r space e g colon I f space w e space t a k e space left parenthesis a comma space b right parenthesis space comma space left parenthesis b comma c right parenthesis space a n d space left parenthesis a comma c right parenthesis space a s space open parentheses 2 comma space 1 third close parentheses space comma space open parentheses 1 third comma space minus 1 close parentheses space a n d space open parentheses 2 comma space minus 1 close parentheses t h e n space left parenthesis a comma b right parenthesis space a n d space left parenthesis b comma c right parenthesis space i s space s a t i s f i e d space b y space R subscript 1 comma space b u t space open parentheses a comma c close parentheses space i s space n o t space s a t i s f i e d space b y space R subscript 1.

Answered by Prasenjit Paul | 2nd Jun, 2015, 10:06: AM