Question

The number of subsets for set A is 512, find the number of elements in it.
$\left( a \right)$ 6
$\left( b \right)$ 7
$\left( c \right)$ 8
\[\left( d \right)\] 9

Answer 1

Hint: In this particular question use the concept that if there are n number of elements in a particular set then there are ${2^n}$ number of subsets for this particular set so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
The number of subsets for set A is 512.
Now we have to find out the number of elements in the set A.
Let there be n number of elements in set A.
So according to property of sets if there are n number of elements in a particular set then there are ${2^n}$ number of subsets.
Therefore, ${2^n}$ = 512
Now factorize 512 we have,
512 = $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
So when 2 multiply by 9 times it gives us 512.
$ \Rightarrow {2^n} = {2^9}$
So on comparing, n = 9.
So there are 9 elements in a set.
So this is the required answer.
Hence option (d) is the correct answer.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall the property of the set which is stated above so simply just substitute the values as above and simplify we will get the required answer.