Question

State whether the following statement is True or False

If n is the number of elements of a set, the number of proper subsets is $2^n-1$

• A. True
• B. False

Answer 1

The correct option is A True

We have to state whether the statement "If $n$ is the number of elements of a set, the number of proper subsets is $2^n-1$" is True or False.
We know that, if a set has $n$ elements then the total number of subsets is $2^n$ including empty set and original set.

A proper subset of a set $A$ is a subset of $A$ that is not equal to $A$.
Thus total number of proper subsets is $2^n-1$ where $-1$ represents the original set.
Hence, if $n$ is the number of elements of a set, the number of proper subsets is $2^n-1$.
Therefore the statement is true.