In Exercises 6 − 10 , a relation R is defined on the set Z of all integers. In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and list at least four members of each. x R y if and only if ( − 1 ) x = ( − 1 ) y .
In Exercises 6 − 10 , a relation R is defined on the set Z of all integers. In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and list at least four members of each. x R y if and only if ( − 1 ) x = ( − 1 ) y .
Solution Summary: The author proves that the relation defined by xRy on the set of all integers Z is an equivalence relation.
In Exercises
6
−
10
, a relation
R
is defined on the set
Z
of all integers. In each case, prove that
R
is an equivalence relation. Find the distinct equivalence classes of
R
and list at least four members of each.
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY