How to deduce the relationship between the number of elements and the number of subsets in a set?

Just give a few examples to deduce.

For example, 1: Find the subset of {0, 1} and the proper subset.

The subsets are: {0}, {1}, {0, 1}, φ, and the number of subsets is 2 n (n is the number of elements).

Proper subset has: {0}, {1}, φ. The number of proper subset is one less in the subset: 2 n- 1.

Example 2: Find the subset of {0, 1, 2} and the proper subset.

These subsets are: {0}, {1}, {2},

{0, 1},{0,2},{ 1,2},

{0, 1,2},φ (2^3=8)

Proper subset: {0}, {1}, {2},

{0, 1},{0,2},{ 1,2},φ (2^3- 1=7)