Let A= {3, 7, 2}.
List all the subsets of A
maybe you want:
3
7
2
3,7
3,2
7,2
number of subsets for 3 elements
= 2^3 = 8
which would include the null set and the entire set.
So we have to include the null set
{}, and the entire set {3,7,2}
To list all the subsets of set A = {3, 7, 2}, we can use the following step-by-step approach:
Step 1: Identify the number of elements in the set A.
A = {3, 7, 2}
Number of elements in A = 3 (denoted by n)
Step 2: Determine the total number of subsets possible for a set with n elements.
The total number of subsets for a set with n elements is given by 2^n.
Step 3: Generate the binary representation of the numbers from 0 to 2^n - 1.
Since n = 3 in this case, the binary representation will include numbers from 000 (0 in decimal) to 111 (7 in decimal).
Step 4: Map each binary number to the elements of the set A.
For each binary number, if the corresponding binary digit is 1, include the corresponding element from the set A. If the binary digit is 0, exclude that element.
The subsets of set A are as follows:
1. Subset with no elements: {}
2. Subset with element 3: {3}
3. Subset with element 7: {7}
4. Subset with element 2: {2}
5. Subset with elements 3 and 7: {3, 7}
6. Subset with elements 3 and 2: {3, 2}
7. Subset with elements 7 and 2: {7, 2}
8. Subset with all elements: {3, 7, 2}
Please note that the order of the subsets listed may vary.
To list all the subsets of a set, you can use the concept of power set. The power set of a set is a set that contains all possible subsets of the original set, including the empty set and the set itself.
In this case, the set A = {3, 7, 2} has three elements. To find the power set, follow these steps:
1. Determine the number of elements in the power set. For a set with n elements, the power set will have 2^n elements.
In this case, A has three elements, so the power set will have 2^3 = 8 elements.
2. Generate binary numbers with n digits. Each binary number corresponds to a subset. The position of a digit in the binary number represents the element's presence or absence in the subset. 0 indicates absence, and 1 indicates presence.
For A = {3, 7, 2}, the binary numbers with three digits are: 000, 001, 010, 011, 100, 101, 110, and 111.
3. For each binary number, include the element at the position where the digit is 1 and exclude it when the digit is 0. This will give you all the subsets of set A.
The subsets of A are:
Subset 1: {}
Subset 2: {2}
Subset 3: {7}
Subset 4: {7, 2}
Subset 5: {3}
Subset 6: {3, 2}
Subset 7: {3, 7}
Subset 8: {3, 7, 2}
So, the subsets of A are {}, {2}, {7}, {7, 2}, {3}, {3, 2}, {3, 7}, and {3, 7, 2}.