If `K = {0,1,2,3}`,then the number of subset =_______

Answer

To find the number of subsets of the set \( K = \{0, 1, 2, 3\} \), we can follow these steps:

### Step 1: Identify the elements in the set
The set \( K \) contains the elements \( 0, 1, 2, 3 \).

### Step 2: Count the number of elements in the set
We count the elements in set \( K \):
- There are 4 elements: \( 0, 1, 2, 3 \).

### Step 3: Use the formula for the number of subsets
The formula for the number of subsets of a set is given by:
\[ \text{Number of subsets} = 2^n \]
where \( n \) is the number of elements in the set.

### Step 4: Substitute the value of \( n \)
In our case, \( n = 4 \) (since there are 4 elements in set \( K \)). Therefore, we substitute \( n \) into the formula:
\[ \text{Number of subsets} = 2^4 \]

### Step 5: Calculate \( 2^4 \)
Now, we calculate \( 2^4 \):
\[ 2^4 = 16 \]

### Conclusion
Thus, the number of subsets of the set \( K \) is \( 16 \).

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