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

Solution:

Given a set has 1024 subsets

A subset means a set in which all the elements are contained in another set.

We know that if a set has n elements, then the total subsets possible are 2ⁿ.

1024 =2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 (using fundamental theorem of arithmetic)

If a set has 1,024 subsets, then it has 2¹⁰

Hence, n = 10 elements.

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

Summary:

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