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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Show that the relation R in the set A of all books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation
Solution:
R = {(x, y) : x and y have same number of pages}
R is reflexive since (x, x) ∈ R as x and x have the same number of pages.
Therefore,
R is reflexive.
(x, y) ∈ R
x and y have the same number of pages and y and x have the same number of pages (y, x) ∈ R
Therefore,
R is symmetric.
(x, y) ∈ R, (y, z) ∈ R
x and y have the same number of pages, y and z have the same number of pages.
Then x and z have the same number of pages.
( x, z ) ∈ R
Therefore,
R is transitive.
R is an equivalence relation
NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 7
Show that the relation R in the set A of all books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation
Summary:
The relation R in the set A of all books in a 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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