Q. 74.3( 69 Votes )
Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.
Answer :
It is given that the set A of all the books in a library of a college. Then,
R = {(x, y): x and y have same number of pages}
Now, R is reflexive
Since, (x,x) ϵ R as x and x have same number of pages.
Let (x,x) ϵ R
⇒ x and y have the same number of pages
⇒ y and x have the same number of pages.
⇒ (y,x) ϵ R
Therefore, R is symmetric.
Now, let (x,y) ϵ R and (y,z) ϵ R
⇒ x and y have the same number of pages and y and z have the same number of pages.
⇒ x and z have the same number of pages.
⇒ (x,z) ϵ R
Therefore, R is transitive.
Therefore, R is an equivalence relation.
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