Let S= {0, 1, 5, 4, 7). Then the total number of subsets of S is

Options

A. 64
B. 32
C. 40
D. 20

Answer

To find the total number of subsets of the set \( S = \{0, 1, 5, 4, 7\} \), we can follow these steps:

### Step 1: Identify the elements of the set
The set \( S \) contains the elements: 0, 1, 5, 4, and 7.

### Step 2: Count the number of elements in the set
Count the elements in the set \( S \):
- There are 5 elements in total: \( 0, 1, 5, 4, 7 \).

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

### Step 4: Substitute the value of \( n \)
Since we have \( n = 5 \) (the number of elements in set \( S \)):
\[ \text{Total subsets} = 2^5 \]

### Step 5: Calculate \( 2^5 \)
Now we calculate \( 2^5 \):
\[ 2^5 = 32 \]

### Conclusion
Thus, the total number of subsets of the set \( S \) is \( 32 \).

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