Sets

We are given two sets: -

A

is the set of even natural numbers less than 8. Therefore,

A%20%3D%20%5C%7B2%2C%204%2C%206%5C%7D

. -

B

is the set of prime numbers less than 7. Therefore,

B%20%3D%20%5C%7B2%2C%203%2C%205%5C%7D

. A relation from set

A

to set

B

is any subset of the Cartesian product

A%20%5Ctimes%20B

, which consists of all possible ordered pairs of elements from

A

and

B

. The number of elements in

A%20%5Ctimes%20B

is the product of the number of elements in

A

and

B

%7CA%20%5Ctimes%20B%7C%20%3D%20%7CA%7C%20%5Ctimes%20%7CB%7C%20%3D%203%20%5Ctimes%203%20%3D%209

The number of relations from

A

B

is the number of subsets of

A%20%5Ctimes%20B

, which is

2%5E%7B%7CA%20%5Ctimes%20B%7C%7D

. Since

%7CA%20%5Ctimes%20B%7C%20%3D%209

, the number of relations is:

2%5E9

Thus, the correct answer is

%5Cboxed%7B2%5E9%7D

Chapter Questions
1 MCQs