Power set and subset: Key differences with examples, worksheet

The Power set and subset both are important topics of the sets in mathematics. Their method of finding is almost the same, but still, there is a major difference between the power set and subset. Today we will discuss the major difference between the power set and the subset with examples.

Difference between power set and subset:

Sometimes students become when the method of finding power set and subset, then why power set and subset are two separate terms? The major difference between the power set and the subset is that subset is further divided into the proper subset and all possible subsets. While the power set always contains all possible sets.

4 differences between power set and subset in points:

In this section, we will take in 4 differences between power set and subset in points

→ Subset is divided into two parts i.e., proper subset and possible subsets.  On the other hand, the power set has all subsets.

→ There is another difference between the power set and the subset is that the representation of both terms is different. The power set is represented by P(S) or P(F) and the subset is represented by “Subset of A, B or C”

→ Subset sometimes includes the given set and sometimes it does not as it depend upon the condition of the question. While the power set is the opposite of it. It includes all the proper and improper subsets.

→ Power set is started and ends with curly brackets ({  }).  

Examples of differences between power set and subset:

We will learn the dissimilarity between the power set and the subset with examples.

Example 1: Find the subset of A={a,e, i}

Solution:

Use this formula: 2ⁿ (where “n” is the number of elements in the above set)

2³=8

A={},{a},{e},{i},{a,e},{a,i},{e,i},{a,e,i}

Example 2: Find the proper subset of A={9,10,11}

Solution:

2³=8 (The proper subset will be one less so the proper subset will be 7)

A={},{9},{10},{11},{9,10},{9,11},{10,11}

The last will be excluded as it is an improper subset.

Example 3: Find the all possible subset of A={c,d,f}

Solution:

Again, Use this formula: 2ⁿ (where “n” is the number of elements in the set)

2³=8

P(A)= {{},{c},{d},{f},{c,d},{c,f},{d,f},{c,d,f}}

Worksheet of power set and subset for practice:

 We are providing some examples of the power sets and the subset for practice. You can do those practice questions to learn the key difference between a power set and a subset in a better way. 

 Find the power set and subset of 

1.{3,9,10}

2.  {7,8,12}

3. {14,21,28}

4. {9,7,8}

5. {b,c,d,f}

6. {b,o,k}

7. {e,f,g,h}

8. {11,12,13,14}

9. {t,u,v,}

10.  {11,22.33}

 

 Thus, we learn the key difference between a power set and a subset with examples in simple language. If you are still confused, then you can comment with us. We will try to solve it.