Question

Let A={Φ,{Φ},{Φ,{Φ}}} and B={1,2}. How many relations from A into B?

Answer 1

Answer: There are 64 relations from A to B.

Explanation:

Number of relation from set A to B =
`2^{\text{ (Number of eklemnts in A x B)}}`

`=2^{\text{(Number of elements in set A ) x (Number of elements in set B)}}`

Since, A={Φ,{Φ},{Φ,{Φ}}} and B={1,2}

i.e. Number of elements in set A = 3

Number of elements in set B = 2

So, Number of relation from set A to B =
`2^(3* 2)`

`= 2^6= 64`

Hence, there are 64 relations from A to B.