CA Foundation Exam > CA Foundation Questions > If R is relation from a finite set A having m...
Start Learning for Free
If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is
- a)2mn
- b)2mn−1
- c)2mn
- d)mn
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If R is relation from a finite set A having m elements to a finite set...
A×B will have mn ordered pairs. Each subset of
A×B will be relation. The number of subsets of a
set consisting of mn elements will be 2mn.
Note : If m=n,then corresponding number will be 2n2.
A×B will be relation. The number of subsets of a
set consisting of mn elements will be 2mn.
Note : If m=n,then corresponding number will be 2n2.
Most Upvoted Answer
If R is relation from a finite set A having m elements to a finite set...
Explanation:
Total number of relations:
- For each element in set A, there are n choices in set B for the first element in the ordered pair.
- Similarly, for the second element in the ordered pair, there are n choices.
- Therefore, for each ordered pair, there are n choices.
- Since there are m elements in set A, the total number of relations is given by n * n * n * ... (m times) = n^m.
Number of relations from A to B:
- Each relation from set A to set B is a subset of the Cartesian product of A and B.
- The Cartesian product of A and B has m * n elements.
- Each subset of the Cartesian product represents a relation from A to B.
- The total number of subsets of a set with k elements is 2^k.
- Therefore, the number of relations from A to B is 2^(m*n).
Hence, the correct answer is option 'A' which is 2^mn.
Total number of relations:
- For each element in set A, there are n choices in set B for the first element in the ordered pair.
- Similarly, for the second element in the ordered pair, there are n choices.
- Therefore, for each ordered pair, there are n choices.
- Since there are m elements in set A, the total number of relations is given by n * n * n * ... (m times) = n^m.
Number of relations from A to B:
- Each relation from set A to set B is a subset of the Cartesian product of A and B.
- The Cartesian product of A and B has m * n elements.
- Each subset of the Cartesian product represents a relation from A to B.
- The total number of subsets of a set with k elements is 2^k.
- Therefore, the number of relations from A to B is 2^(m*n).
Hence, the correct answer is option 'A' which is 2^mn.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer?
Question Description
If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer?.
If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If R is relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B isa)2mnb)2mn−1c)2mnd)mnCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup