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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.

Q.7 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.

Answers (1)
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 A = all the books in a library of a college

R = \{(x, y) : x \;and\;y\;have\;same\;number\;of\;pages\}

(x,x) \in R  because  x and x have same number of pages so it is reflexive.

Let  (x,y) \in R  means x and y have same number of pages.

Since,y and x have same number of pages so  (y,x) \in R  .

Hence, it is symmetric.

Let  (x,y) \in R  means x and y have same number of pages.

 and  (y,z) \in R  means y and z have same number of pages.

This states,x and z also have same number of pages i.e.(x,z) \in R

Hence, it is transitive.

Thus, it is reflexive, symmetric and transitive i.e. it is an equivalence
relation.?

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