Question

If A is {{0}, {0, {0}}}, then the power
set of A has how many element?​

Answer 1

Answer:

4

Explanation:

Answer 2

The power set of A has 4 elements

Given :

A = { {0} , {0, {0}} }

To find :

The number of elements in power set of A

Solution :

Step 1 of 3 :

Write down number of elements in A

Here the given set is

A = { {0} , {0, {0}} }

The elements of A are {0} , {0, {0}}

So A has two elements

Step 2 of 3 :

Define power set of a set

The collection of all subsets of a non empty set A is a set of sets. This set is called the power set A and is denoted by P(A)

Let the number of elements in the set A = n

Then number of elements in power set of A = 2ⁿ

Step 3 of 3 :

Calculate the number of elements in power set of the given set

Since the number of elements in the set A = 2

∴ The number of elements in power set of A

$\displaystyle \sf{ = {2}^{2} }$

$\displaystyle \sf{ } = 4$

More Precisely ,

P(A) = { Φ , {{0}} , {{0, {0}}} , { {0} , {0, {0}} } }

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