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If A is the set of even natural number less than 8 and B is the set of prime number less than 7, then number of relations from A to B is
- a)29
- b)92
- c)32
- d)29-1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If A is the set of even natural number less than 8 and B is the set of...
A = {2,4,6}, B = {2,3, 5}
So, A x B contains 3 x 3 = 9 elements.
Hence, number of relations from A to B = 29.
So, A x B contains 3 x 3 = 9 elements.
Hence, number of relations from A to B = 29.
Most Upvoted Answer
If A is the set of even natural number less than 8 and B is the set of...
To find the number of relations from set A to set B, we need to determine the number of ordered pairs (a, b) where a is an element of A and b is an element of B.
Given that set A consists of even natural numbers less than 8, we have A = {2, 4, 6}.
And set B consists of prime numbers less than 7, we have B = {2, 3, 5}.
To form an ordered pair (a, b), we can choose any element from set A as the first element (a) and any element from set B as the second element (b).
Total number of choices for the first element (a):
Since A has 3 elements, we have 3 choices for a.
Total number of choices for the second element (b):
Since B has 3 elements, we have 3 choices for b.
Since the choices for a and b are independent, the total number of ordered pairs (a, b) is obtained by multiplying the number of choices for a and b.
Total number of ordered pairs = 3 * 3 = 9
However, we need to consider that there may be some ordered pairs that are repeated.
To determine the number of repeated ordered pairs, we observe that both sets A and B have the common element '2'.
Number of repeated ordered pairs = Number of elements in A that are common with B = 1
Therefore, the number of distinct ordered pairs (a, b) is obtained by subtracting the number of repeated ordered pairs from the total number of ordered pairs.
Number of distinct ordered pairs = Total number of ordered pairs - Number of repeated ordered pairs = 9 - 1 = 8
Hence, the correct answer is option 'A' which is 8.
Given that set A consists of even natural numbers less than 8, we have A = {2, 4, 6}.
And set B consists of prime numbers less than 7, we have B = {2, 3, 5}.
To form an ordered pair (a, b), we can choose any element from set A as the first element (a) and any element from set B as the second element (b).
Total number of choices for the first element (a):
Since A has 3 elements, we have 3 choices for a.
Total number of choices for the second element (b):
Since B has 3 elements, we have 3 choices for b.
Since the choices for a and b are independent, the total number of ordered pairs (a, b) is obtained by multiplying the number of choices for a and b.
Total number of ordered pairs = 3 * 3 = 9
However, we need to consider that there may be some ordered pairs that are repeated.
To determine the number of repeated ordered pairs, we observe that both sets A and B have the common element '2'.
Number of repeated ordered pairs = Number of elements in A that are common with B = 1
Therefore, the number of distinct ordered pairs (a, b) is obtained by subtracting the number of repeated ordered pairs from the total number of ordered pairs.
Number of distinct ordered pairs = Total number of ordered pairs - Number of repeated ordered pairs = 9 - 1 = 8
Hence, the correct answer is option 'A' which is 8.
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If A is the set of even natural number less than 8 and B is the set of prime number less than 7, then number of relations from A to B isa)29b)92c)32d)29-1Correct answer is option 'A'. Can you explain this answer?
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