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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?
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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.
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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?
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