Write down all possible subsets of each of the sets given below :
{a,b,c,d}

Answer

To find all possible subsets of the set {a, b, c, d}, we can follow these steps:

### Step 1: Understand the concept of subsets
A subset is a set that contains some or all elements of another set. The empty set is also considered a subset.

### Step 2: Count the number of subsets
For a set with 'n' elements, the total number of subsets is given by the formula \(2^n\). In this case, the set {a, b, c, d} has 4 elements, so the total number of subsets is \(2^4 = 16\).

### Step 3: List all subsets
We can systematically list all subsets, starting from the empty set and moving to the full set:

1. Empty set: {}
2. Subsets with one element: {a}, {b}, {c}, {d}
3. Subsets with two elements: {a, b}, {a, c}, {a, d}, {b, c}, {b, d}, {c, d}
4. Subsets with three elements: {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}
5. Full set: {a, b, c, d}

### Step 4: Compile the list of all subsets
Now, we can compile all the subsets we have listed:

- {}
- {a}
- {b}
- {c}
- {d}
- {a, b}
- {a, c}
- {a, d}
- {b, c}
- {b, d}
- {c, d}
- {a, b, c}
- {a, b, d}
- {a, c, d}
- {b, c, d}
- {a, b, c, d}

### Final Answer
The complete list of all possible subsets of the set {a, b, c, d} is:
1. {}
2. {a}
3. {b}
4. {c}
5. {d}
6. {a, b}
7. {a, c}
8. {a, d}
9. {b, c}
10. {b, d}
11. {c, d}
12. {a, b, c}
13. {a, b, d}
14. {a, c, d}
15. {b, c, d}
16. {a, b, c, d}