Question

If a set has 1,024 subsets, how many elements does it have?

Answer 1

If a set has 1,024 subsets,then it has 10 elements

Explanation:

If A is a set containing n elements then total numbers of subsets of A are
`2^n`

Here, we are given that

`2^n=1024`

We know that

`1024=2^(10)`

i.e.
`2^n=2^(10)`

Hence, n=10

Hence, If a set has 1,024 subsets,then it has 10 elements