Q. 214.9( 7 Votes )

Express <im

Answer :

Given: where;


To Find: Express it in the simplest form.






OR


Given: R = {(a, b): 2 divides a – b}


To Find: (i) Relation R is transitive or not.


(ii) Equivalent class [0]


The relation given is R = {(a, b): 2 divides a – b}


If we consider 2 divides b – c


So, 2 divides (a – b) + (b – c) = (a – c) where a, b, c R


So, the relation is transitive. [Proved]


Equivalence class [0], means that one element is 0, we need to find other elements which satisfy R.


The relation, R = {(a, b): 2 divides a – b}


Here b = 0, so, the relation becomes, R = {(a, 0): 2 divides a – 0}


To satisfy the relation, possible values of a are 0, 2, 4, …, i.e., all the even numbers and 0.


Therefore, the equivalence class [0] = {0, 2, 4, …}


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