Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Let R= { ( a,a ), ( b,c ), ( a,b ) } be a relation on a

Question

Let $R = {(a, a), (b, c), (a, b)}$ be a relation on a set $A = {a, b, c} .$ Then the minimum number of ordered pairs which when added to R make it an equivalence relation are ...

Views: 539 students

Found 7 tutors discussing this question

Harper Discussed

Let

R = {(a, a), (b, c), (a, b)}

be a relation on a set

A = {a, b, c} .

Then the minimum number of ordered pairs which when added to R make it an equivalence relation are ...

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

{(b, b), (c, c), (b, a), (c, b), (a, c), (c, a)}

R = {(a, a), (b, c), (a, b)}

For relexive add

(b, b), (c, c) .

∴ R = {(a, a), (b, c), (a, b) (b, b) (c, c) (c, b), (b, a)} (a, b) ϵ R (b, c) ϵ R

so that (a,c) must belong to R.
Hence we must add (a,c) and for symmetric we must add (c,a) also.

∴ R {(a, a), (b, c), (a, b) (b, b), (c, c), (c, b), (b, a) (a, c) (c, a)}

Ans: 6

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our maths tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Let $R = {(a, a), (b, c), (a, b)}$ be a relation on a set $A = {a, b, c} .$ Then the minimum number of ordered pairs which when added to R make it an equivalence relation are ...
Answer Type	Text solution:1
Upvotes	150