Question
In the set of all integers, which of the following relation is an equivalence relation?
Found 4 tutors discussing this question
Discuss this question LIVE
5 mins ago
Text solutionVerified
For option C, xRy:if x-y is an even integer .
Let a be any number in Z,
Then, a-a=0 is an even integer .
So, Every number is related to itself .
Thus the relation is reflexive .
Let a,b be two numbers in Z,
Also let be an even integer (which implies aRb)
Then, is also an even integer (which implies bRa).
Thus, It is evident
Thus the relation is also symmetric .
Let a,b,c be three numbers in Z,
Also let aRb and bRc,
then and for belonging to Z
which gives
which implies .
Thus relation is also transitive .
Thus we finally arrive at a conclusion that relation is Equivalence relation .
Was this solution helpful?
150
Share
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
Practice questions from similar books
Question 1
For real number and , define a relationship {; if and only if is an irrational number }. Then the relation isStuck 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 | In the set of all integers, which of the following relation is an equivalence relation? |
Answer Type | Text solution:1 |
Upvotes | 150 |