Question

Number of non empty subsets of the set consisting $10$ elements in all, is

• A. $1023$
• B. $1024$
• C. $2^{10}-2$
• D. $2^9$

Answer 1

The correct option is A $1023$

Let $A$ is a set consisting $10$ elements

$\therefore n\left(A\right)=10$

Now number of subsets of a set having n elements $=2^n$

$\therefore$ Number of subsets of given set $A=2^{10}$

Now in these subsets there is only one empty set which is subset of $A$

$\therefore$ Number of non-empty subsets are $2^{10}-1=1023$