Subsets

A set N is a subset of a set X, if all the elements of N are contained in/members of the larger set X.

Example
If, X = {3, 5, 6, 8, 9, 10, 11, 13}
And, N = {5, 11, 13}
Then, N is a subset of X.
That is, N ⊂ X (where ⊂ means ‘is a subset of’).

Number of Subsets

If, M = {a, b, c}
Then, the subsets of M are:
{a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}, {}
Therefore, the number of subsets, S = 8

And the formula, S = 2ⁿ
Where,
S is the number of sets
And, n is the number of elements of the set
Is the formula used to calculate the number of subsets of a given set.

So from above, M = {a, b, c}
S = 2ⁿ
= 2³
= 2 x 2 x 2
= 8

Note: Every set is a subset of itself, and the empty set is a subset of all sets.