Subset Calculator

Subset Calculator

Subset calculator is used to evaluate the possible subsets of the given set. This subsets calculator finds the subsets of sets up to 10 elements along with steps. 

What is a Subset?

A subset is defined as the elements of any set “A” are also elements of another set “B”.  In other words, one set (say A) is a subset of another set (say B) if all of its elements are contained within the other set

The mathematical symbol used to represent the subset is “⊆”. Such as if a set A is a subset of another set B that can be represented as “A ⊆ B” which reads as “A is the subset of B”.

• The formula used to find the possible number of the subset is 2n 
• The formula used to find the possible number of proper subsets is 2n - 1

Note:

The empty set is represented by the “{ } or ∅”

Examples of Subsets

Example 1:

Evaluate all subsets of the given set.

If A = {2, 3, 4, 5, 23}.

Solution:

Step 1: Count the elements of the given set and find the number of possible subsets by applying the formula.

n = 5

Possible number of subset = 2ⁿ

Possible number of subset = 2⁵ = 32

Step 2: Write all possible subsets.

{} , {2} , {3} , {4} , {5} , {23} , {2,3} , {2,4} , {3,4} , {2,5} , {3,5} , {4,5} , {2,23} , {3,23} , {4,23} , {5,23} , {2,3,4} , {2,3,5} , {2,4,5} , {3,4,5} , {2,3,23} , {2,4,23} , {3,4,23} , {2,5,23} , {3,5,23} , {4,5,23} , {2,3,4,5} , {2,3,4,23} , {2,3,5,23} , {2,4,5,23} , {3,4,5,23} , {2,3,4,5,23}.

Example 2:

Determine the possible number of subsets and proper subsets if a set has 7 elements.

Solution:

Step 1: Find the number of possible subsets by applying the formula.

Possible number of subset = 2ⁿ

Possible number of subset = 2⁷

Possible number of subsets = 128

Step 2: Find the number of possible proper subsets by applying the formula.

Possible number of proper subset = 2ⁿ -1

Possible number of proper subset = 2⁷ -1 = 128 - 1

Possible number of proper subsets = 127