# How To Calculate Number of Proper Subsets of a Set?

Short tutorial that explains you on how to calculate number of proper subsets of a set explained with a simple example in a step by step procedure.

## Proper Subsets of a Set Calculation

Number of Proper Subsets of a Set is that, If a set contains "n" elements, then the number of proper subsets of the set is 2^{n}- 1.

Suppose, if A = {i, j} the proper subsets of A are [{ }, {i}, {j}]

→Â Number of proper subsets of A = 2^{2 }- 1 = 4 - 1 = 3

Let us learn how to calculate number of proper subsets of a set with a neat example here.

**Formula:**

**Number of Proper Subsets of a Set = 2**^{n}- 1

For example, If A = {1, 2, 3, 4, 5}, Calculate Number of Proper Subsets of a Set.

**Step 1:** Given,

A = {1, 2, 3, 4, 5}

n = 5

**Step 2:** Applying the values in the formula,

Number of proper subsets of A = 2^{5 }- 1 = 32 - 1 = 31

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