### 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 = 2^{n}

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 = 2^{n}

= 2^{3}

= 2 x 2 x 2

= 8

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