Question

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show that the relation R in the set A of all books in library of a college, given by R={(x,y):x and y have same number of pages} is an equivalence relation

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Answer 1

Answer:

here is your answer xD

It is given that R = {(x, y): x and y have the same number of pages}. We have to show that this is an equivalence relation, that is it is reflexive, symmetric and transitive. ... Any book will have the same number of pages as itself, hence R is a reflexive relation.

Answer 2

Set A is the set of all books in the library of a college.

R = {x, y): x and y have the same number of pages}

Now, R is reflexive since (x, x) ∈ R as x and x has the same number of pages.

Let (x, y) ∈ R ⇒ x and y have the same number of pages.

⇒ y and x have the same number of pages.

⇒ (y, x) ∈ R

∴R is symmetric.

Now, let (x, y) ∈R and (y, z) ∈ R.

⇒ x and y and 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) ∈ R

∴R is transitive.

Hence, R is an equivalence relation.