Question

If a set has n elements, then it has ____ subsets.

• A. n
• B. n²
• C. 2ⁿ
• D. 2n

Answer 1

The correct option is C

2ⁿ

If set A has one element, A = {a}

Subsets of A are { } and {a}. Thus set A has 2, i.e. $2^1$ subsets.

If set A has two elements, A = {a, b}

Subsets of A are { }, {a}, {b}, {a,b}. Thus set A has 4, i.e. $2^2$ subsets.

If set A has three elements, A = {a, b,c}

Subsets of A are { }, {a}, {b}, {c}, {a,b},{b, c}, {c, a}, {a, b, c}. Thus set A has 8, i.e. $2^3$ subsets.

If a set A has n elements, then A will have $2^n$ subsets.