Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
0 votes

Let \(A = \{1, 2, 3\}.\) Then number of equivalence relations containing \((1, 2)\) is

$\begin{array}{1 1} 1 \\ 2 \\ 3 \\ 4 \end{array}$

Can you answer this question?

1 Answer

0 votes
  • A relation R in A is an equivalence relation if it is,reflexive,symmetric and transitive.
The smallest equivalence relation containing (1,2) is $R=\{(1,1),(2,2),(3,3),(1,2)(2,1)\}$
To get another relation which is equivalence can be done by adding the remaining pairs $(2,3),(3,2),(1,3),(3,1)$ to get the universal relation.
This shows that there are only 2 equivalence relation containing (1,2)
Hence correct answer is B
answered Feb 28, 2013 by meena.p
edited Mar 20, 2013 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App