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Show that the relation R in the set A of all the books in a library of...

Show that the relation R in the set A of | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question: 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:

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.

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Popular questions of class 12 Mathematics

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 1 , Question 7: Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, ....

Show that the relation R in the set A of | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

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