Question

the number of proper subsets of the X = { x2: x € N, x2 < 100}.
​

Answer 1

the following set in roster form is

X={1,4,9,16,25,36,49,64,81}

There are 9 elements in this set

$numberof \: proper \: subsets \\ = {2}^{n} - 1 \\ = {2}^{9} - 1 \\ = 512 - 1 \\ = 511$