Power Set with Examples

In this class, We discuss Power Set with Examples.

The reader should have prior knowledge of set theory basics. Click Here.

Power set:

The collection of all subsets of a set A is called a power set.

Power set denoted by ρ(A)

Example:

A = {a, b, c}

ρ(A) = {Φ, {a}, {b}, {c}, {a,b}, {a,c}, {b, c}, {a, b, c}}

Example:

A = {a, {b})

ρ(A) = {Φ, {a}, {{b}}, {a, {b}}}

A has n elements

ρ(A) has 2^n elements.

Power set of an empty set:

A = { }

ρ(A) = {Φ}

ρ(ρ(A)) = {Φ, {Φ}}

ρ(ρ(ρ(A))) = (Φ, {Φ}, {{Φ}}, {Φ,{Φ}}}