If A is the set of evern natural number less than 8 and B is the set of prime numbers less than 7. Then number of relation from A to B isa)29b)92c)32d)23-1Correct answer is option 'A'. Can you explain this answer?

Question

Answer

A={2,4,6},B={2,3,5}
Number of relations = 2mn

m = 3, n = 3

Number of relations from A to B is 2^9

Answer

A = {2, 4, 6

B = {2, 3, 5}

Number of relations = 2

mn

m = 3, n = 3

2

9

is the correct answer.

Answer

A
is the answer

Answer

A is right

Answer

To find the number of relations from set A to set B, we need to consider the number of possible ordered pairs that can be formed using the elements of A and B.

Set A consists of even natural numbers less than 8: A = {2, 4, 6}

Set B consists of prime numbers less than 7: B = {2, 3, 5}

The number of ordered pairs that can be formed is equal to the product of the number of elements in A and the number of elements in B.

Number of elements in A = 3
Number of elements in B = 3

Therefore, the number of ordered pairs = 3 * 3 = 9

However, we need to consider the fact that a relation can have multiple ordered pairs with the same first element but different second elements.

Let's consider the elements of A one by one and count the possible ordered pairs for each element:

For the element 2 in A, there are 3 possible ordered pairs since 2 can be related to any of the 3 elements in B: (2, 2), (2, 3), (2, 5)

For the element 4 in A, there are 3 possible ordered pairs as well: (4, 2), (4, 3), (4, 5)

For the element 6 in A, there are 3 possible ordered pairs: (6, 2), (6, 3), (6, 5)

So, in total, there are 3 ordered pairs for each element of A, and since A has 3 elements, the total number of ordered pairs is 3 * 3 = 9.

However, we need to subtract the cases where the first and second elements are the same since the question asks for a relation from A to B, not a relation from A to A.

For the element 2 in A, there is one ordered pair where the first and second elements are the same: (2, 2)

For the element 4 in A, there is no ordered pair where the first and second elements are the same.

For the element 6 in A, there is no ordered pair where the first and second elements are the same.

So, we need to subtract 1 from the total number of ordered pairs: 9 - 1 = 8.

Therefore, the number of relations from A to B is 8, which matches with option A.

Answer

Concept:
A non-empty subset H of a group (G, ∗) is a group of G iff,
⇒ a, b ∈ H ⇒ a ∗ b^-1 ∈ H

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