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If n(A) = p and n(B) = q, then how many relations are there from A to B.
- a)pq
- b)3pq
- c)2pq
- d)(pq)2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If n(A) = p and n(B) = q, then how many relations are there from A to ...
Number of relation from A to B = 2n(A)×n(B)
n(A) = p, n(B) = q
⇒ Number of relation from A to B = 2pq
⇒ Number of relation from A to B = 2pq
Community Answer
If n(A) = p and n(B) = q, then how many relations are there from A to ...
Solution:
The term 'relation' refers to a set of ordered pairs where the first element belongs to A and the second element belongs to B.
To find the total number of relations from A to B, we need to consider all possible combinations of pairs of elements from A and B.
For each element in A, we can choose any element from B to form a pair. Since there are q elements in B, we have q choices for each element in A. Therefore, the total number of possible pairs is p*q.
Since each set of ordered pairs represents a unique relation, the total number of relations from A to B is equal to the total number of possible pairs, which is p*q.
Hence, the correct option is C) 2pq.
The term 'relation' refers to a set of ordered pairs where the first element belongs to A and the second element belongs to B.
To find the total number of relations from A to B, we need to consider all possible combinations of pairs of elements from A and B.
For each element in A, we can choose any element from B to form a pair. Since there are q elements in B, we have q choices for each element in A. Therefore, the total number of possible pairs is p*q.
Since each set of ordered pairs represents a unique relation, the total number of relations from A to B is equal to the total number of possible pairs, which is p*q.
Hence, the correct option is C) 2pq.
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