Question

Write power sets of the following $\{ 1,2,3\} $

Answer 1

Hint: Power set of any given set can be defined as the set which includes all the subsets including the empty set and the original set itself. For the power set of A, it is denoted by P(A). Here we will take the given set and will find the power sets of it.

Complete step-by-step answer:
Let us assume that the given set is denoted by A.
Therefore, $A = \{ 1,2,3\} $
Now, the number of sets in the power sets can be given by ${2^n}$ where “n” is the total number of elements in the set.
So, here the total number of elements are three and therefore ${2^3} = 8$
Now, the power sets of the given expression using the concepts of subsets can be given by –
$P(A) = \{ 1\} ,\{ 2\} ,\{ 3\} ,\{ 1,2\} ,\{ 1,3\} ,\{ 2,3\} ,\{ 1,2,3\} ,\{ \} $
This is the required solution.
So, the correct answer is “$P(A) = \{ 1\} ,\{ 2\} ,\{ 3\} ,\{ 1,2\} ,\{ 1,3\} ,\{ 2,3\} ,\{ 1,2,3\} ,\{ \} $”.

Note: Always check the power sets and its count by using the formula. Subsets can be defined as the part of the mathematical concepts known as sets. A set can be defined as the collection of elements which are grouped in the curly brackets. Let us assume if A is the collection of all odd numbers and the set B consists of $\{ 1,3,5\} $ then B is said to be the subset of A.