Question

The number of subsets of the set $A=\{a_1,a_2,.........a_n\}$ which contain even number of elements is

• A. $2^{n-1}$
• B. $2^n-1$
• C. $2^n-2$
• D. $2^n$

Answer 1

The correct option is A $2^{n-1}$

The total no of subsets of $A$ is the cardinality of the power set of $A$.

So, if $|A|=n$ then $|P\left(A\right)|=2^n$.

Therefore total no of subsets of $A$ is $2^n$.

Similarly,

The even number of events is given by, $2^{n-1}$