Let S be a relation on the set R of all real numbers defined by
S space equals space left curly bracket left parenthesis a comma space b right parenthesis element of R asterisk times R space colon thin space a squared plus b squared equals 1 right curly bracket
Prove that S is not an equivalence relation on R.

Asked by abhinavsaini123 | 1st Jun, 2015, 08:55: PM

Expert Answer:

S equals open curly brackets left parenthesis a comma b right parenthesis space element of R colon space a squared plus b squared equals 1 close curly brackets  L e t space a space b e space a space n u m b e r space o n space R F o r space r e f l e x i v i t y comma W e space h a v e space t o space p r o v e comma a squared plus a squared equals 1 2 a squared equals 1 a equals fraction numerator 1 over denominator square root of 2 end fraction B u t space f o r space a equals 1 half comma open parentheses 1 half comma 1 half close parentheses left right double arrow open parentheses 1 half close parentheses squared plus open parentheses 1 half close parentheses squared not equal to 1  therefore space T h e space r e l a t i o n space i s space n o t space r e f l e x i v e. H e n c e comma space i t space i s space n o t space a n space e q u i v a l e n c e space r e l a t i o n.

Answered by Prasenjit Paul | 2nd Jun, 2015, 10:22: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.