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CBSE Class 12-science Answered

<div>please help me to solve it in detail....</div> <div>&nbsp;</div> <div><img 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" alt="" width="527" height="54" /></div>
Asked by nitishkrnehu09 | 16 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
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