please help me to solve it in detail....
 

Asked by nitishkrnehu09 | 16th Nov, 2017, 07:57: AM

Expert Answer:

begin mathsize 16px style Consider comma space left parenthesis straight a comma straight b right parenthesis space left parenthesis straight c comma straight d right parenthesis comma space left parenthesis straight e comma straight f right parenthesis space element of space straight N cross times straight N
straight a plus straight b equals straight b plus straight a space for space all space straight a comma straight b element of straight N space using space commutativity space law space of space addition space in space straight N
It space is space reflexive.
For space left parenthesis straight a comma straight b right parenthesis space straight R space left parenthesis straight c comma straight d right parenthesis space rightwards double arrow space straight a plus straight d equals straight b plus straight c space rightwards double arrow space straight d plus straight a equals straight c plus straight b
Hence space it space is space symmetric
For space left parenthesis straight a comma straight b right parenthesis space left parenthesis straight c comma straight d right parenthesis comma space left parenthesis straight e comma straight f right parenthesis space element of space straight N cross times straight N
straight a plus straight d equals straight b plus straight c space and space straight c plus straight f equals straight d plus straight e
rightwards double arrow straight a plus straight d plus straight c plus straight f equals straight b plus straight c plus straight d plus straight e
Hence space it space is space transitive.

To space find space equivalence space class space left square bracket left parenthesis 1 comma 3 right parenthesis right square bracket
class space of space element space of space left parenthesis 1 comma 3 right parenthesis
left parenthesis straight a comma straight b right parenthesis space straight R space left parenthesis 1 comma 3 right parenthesis space rightwards double arrow straight a plus 3 equals straight b plus 1
rightwards double arrow straight b equals straight a plus 2 space but space straight a comma straight b element of straight A space straight a comma straight b element of open curly brackets 1 comma 2 comma 3 comma 4 close curly brackets
So space we space take space straight a equals 1 comma 2 comma 3 comma 4 space then space the space corresponding space values space of space straight b space are
3 comma 4 comma 5 comma 6
Equivalence space class space left square bracket left parenthesis 1 comma 3 right parenthesis right square bracket equals open curly brackets left parenthesis 1 comma 3 right parenthesis comma left parenthesis 2 comma 4 right parenthesis comma left parenthesis 3 comma 5 right parenthesis comma left parenthesis 4 comma 6 right parenthesis close curly brackets end style

Answered by Sneha shidid | 7th Dec, 2017, 02:18: PM